Probability and Statistics: Statistics Word Problems

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Probability and Statistics

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Mean

Mean in probability and statistics.

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Median in probability and statistics.

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Standard Deviation

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Probability and Statistics: Statistics Word Problems

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Probability and Statistics: Statistics WordProblems

There are four choices of apple and orange
There are four choices of apple and ...
11 people are racing
11 people are racing. What are the odds of being 1...
How many 3 topping pizzas
How many 3 topping pizzas could be made if you have 10 toppings to choose from?
A cheese pizza can be ordered
A cheese pizza can be ordered with some, all, or none of the following toppings: sausage, pepperoni, ham, peppers, mushrooms, olives, anchovies, pineapple, and ...
A mall has 12 clothing stores
A mall has 12 clothing stores, 9 shoe stores and 5 electrical stores. In how many ways can a person shopping at this mall go to 5 clothing ...
Find the IQ score separating the top
Find the IQ score separating the top 85% from the ...
Test for high school students
Test for high school students with a 3.50 to 4.00 grade point average were normally distributed, with a mean of 38.8 and a standard diviation of 1.9. A student with a 3.5 to 4.00 grade point average who took the standarized tes is randomly ...
30% of a firm`s orders come from new customers
30% of a firm's orders come from new customers. A simple random sample of 100 orders will be used to estimate the proportion of new customers. Find probability that sample proportion will be between 0.22 and 0...
A normal distribution has a mean
A normal distribution has a mean of 80 and a standard deviation of 14...
A pediatrician`s records show
A pediatrician's records show that height of a random sample 25 girls at age 12 months to be 29.530 inches with a standard deviation of 1.0953 ...
In France, years of life expectancy
In France, years of life expectancy are normally distributed with a mean of 81 years and a standard deviation fo seven years. For the French population:
a) What is the probability of living 92 years or ...
John wants to paint four rooms
John wants to paint four rooms in his house, each a different color and he may choose from seven different colors of ...
In how many different ways
In how many different ways can 11 different books be distributed to ...
In a class of 25 students
In a class of 25 students, the grades were normally distributed with a mean of 78 and a standard deviation of 5. Sketch the normal curve for the distribution. What percentage of the students scored above an 88...
There are three sections of science class available
There are three sections of science class available at the convinient times for student. There is 24% chance from Professor Praful to give final exam, 15% chance for professor Ron, and 8% chance for Professor Sam to give final exam. At other times there are two maths classes, and in those the probability to give final exam is 2% and 10%...
A bag contains 6 blue discs
A bag contains 6 blue discs, 10 orange discs and 4 red discs. If a disc is picked at random, what is the probability of getting :
a ...
Selena has 4 exams
Selena has 4 exams ( A, B, C,D) to study for this ...
A barrel contains only apples and oranges
A barrel contains only apples and oranges. There are twice as many apples as oranges. The apples are either red or yellow and 4 times as many red as are yellow. If one piece of fruit is to be drawn at random from the ...
Three apples cost as much as four pears
Three apples cost as much as four pears. 3 pears cost as much as 2 ...
A bag of jelly beans contains
A bag of jelly beans contains 12 cherry, 15 lemon, 17 lime, 13 strawberry, and 18 orange jelly ...
A bag contains 6 green marbles
A bag contains 6 green marbles, 6 blue marbles, 5 yellow marbles , 13 red marbles, and 10 purple ...
Lisa is planning the seating
Lisa is planning the seating for a head table at a gala. The eight speakers will all be seated along one side of the table. Richard wants to be sit beside Hang, and lisa knows that Thomas and Lily should not be seated together, as they have just broken ...
There are 4 digits on a lock
There are 4 digits on a ...
There are 3 entrances and 3 exits
There are 3 entrances and 3 exits to a large parking ...
Have 8 navy blue socks
Have 8 navy blue socks, 5 black ...
A drawer contains 8 black socks
A drawer contains 8 black socks, 18 green socks, 12 blue socks and 11 brown socks. If the drawer is in a darkened ...
A container of jelly beans contains
A container of jelly beans contains 50 buttered popcorn, 65 strawberry, 80 cinnamon, and 45 ...
At the picnic, there is a plate
At the picnic, there is a plate of 3 dill pickles, 2 bread and butter pickles, and 1 sweet ...
A spinner is divided into five equal sections
A spinner is divided into five equal sections numbered 1 through 5...
A bowl with 2 yellow marbles
A bowl with 2 yellow marbles, 1 blue and 2 red. If you pick one marble from the bowl ...
The mayor of a small town estimates
The mayor of a small town estimates that 35% of the residents in his town favor the construction of a municipal parking lot. If there are 350 people at a town meeting, find the probability that at least 100 favor construction of a parking lot. Based on your ...
A manufacturer of automobile batteries
A manufacturer of automobile batteries claims that the average length of life for its grade "A" battery is 60 months. However the guarantee on this brand is just for 36 months. Suppose the standard deviation of the life length is known to be 10 ...
With a height of 69 inches, Alexander was the shortest
With a height of 69 inches, Alexander was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 75.4 inches and a standard deviation of 2.7.
a. What is the difference between Alexander's height and the mean?
...
Drawing 3 cards that are all aces
Drawing 3 cards that are all aces from a deck of cards?
probability
Two cards are simultaneously drawn from an ordinary ...
There are 3 bags of apples
There are 3 bags of apples, one has two green apples, one has two red apples and one has 1 green and 1 red apple.  All three bags are mislabeled.  You may look at only one apple from any one of the ...
probability
29 out of 200 chickens contaminated.  If chicken infected, test will return positive 80% of the time.  If chicken not infected, test will return "false" positive 5% of the time.

If test is ...
You have twenty-two socks
You have twenty-two socks. Fortunately, you only have two colors white and ...
A student notices that if he is late
A student notices that if he is late for college on one day, he is three times more likely to be late on the next day. If he is early on one day, he is equally likely to be early or late on the next day.

Draw a tree diagram to show all the possible outcomes for three successive days. ( Assume that the student was early on the day before the 3 days under consideration.)
If there are 25 names in a hat
If there are 25 names in a hat, 15 girl’s names and 10 boy’s names, what is the probability that a name drawn at random will be
I. a girl’s name
II. a boy’s name
III. not a girl’s name
IV. not a boy’s name
If the chances of snow or sleet last Saturday
If the chances of snow or sleet last Saturday was three out of ten and the chance of snow or sleet this Saturday was four out of ten what were the chances of snow or sleet happening both weeks?
Kate has a red pair of shoes
Kate has a red pair of shoes, a blue pair of shoes, and a green pair of shoes. She has a yellow and an orange ...
A reading program is administered
A reading program is administered to the bottom 5% of the students. If the average score of the students is 122.6, find the cutoff score that will make a student eligible to the ...
At a fair, 37 pumpkins were entered for judging
At a fair, 37 pumpkins were entered for judging under the normal pumpkin division. If the masses are normally distributed and the average weight is 12.4 kg, with a standard deviation for 2.31 kg. What is the probability that a pumpkin has a mass between 13...
What is the probability of obtaining a sum
What is the probability of obtaining a sum of at least 6 when rolling a pair of dice?
An airplane has two independent alternators
An airplane has two independent alternators to provide electrical power. The probability that a given alternator wil fail on a one hour flight is .02...
Of the 148 students honored at an academic banquet
Of the 148 students honored at an academic banquet, 40 won awards for mathamatics and 82 for English. One of the 148 students is chosen at random to be inter viewed for a newspaper article. What is the probability that the student won an award in matematics or ...
In a certain high school 65% of students
In a certain high school 65% of students own cell phonoes. 35% own MP3 players. 20% own both cell phones and MP3 players. Identify the probability that a student has either a ceell phone or an MP3 players. Identify the paobaility that a student has only an MP3 ...
Jim sells soup at his stand
Jim sells soup at his stand. He sells lentil, split pea, and navy bean soup. They also come in four different ...
In a fair game two guys bet
In a fair game (50/50 chance of winning) two guys bet $100 each. The first one to win 6 games takes the pot. They decided to stop when A had won 5 games and B had won 3 ...
What is the probability of drawing two cards
What is the probability of drawing two cards that are not in the same suit when drawn simultaneously?
What is the critical z-value
What is the critical z-value that corresponds to a confidence level of 86%
There are 3 sky blue marbles
There are 3 sky blue marbles and 3 hot pink marbles in a bag. What is the probability that I will draw out 1 sky blue ...
After 4 games, Rita`s average
After 4 games, Rita's average bowling score was 99...
During a root enzyme experiment
During a root enzyme experiment, Grace determined the dry weight of mustard roots so she could make some calculations. These were pretty small mustard plants so she had to use a good balance to get the data. She measured one set (A) of roots and obtained masses of 0.06, 0.09, 0.08, 0.05, and 0.05 grams. Another set (B) had masses of 0.1, 0.11, 0.09, 0.11, and 0.04 ...
If the life, in years, of a washing machine
If the life, in years, of a washing machine is normally distributed with a mean of 20 years and a standard deviation of 1.5 ...
Renee ran the marathon in 3 hours
Renee ran the marathon in 3 hours. If she ran 10 miles in the first hour, what was her average speed, in miles per ...
A whole sale distributor has found
A whole sale distributor has found that the amount of a customer's order is a normal random variable with a mean of $200 and a standard deviation of $50...
The temperatures for last week in Columbus, Ohio
The temperatures for last week in Columbus, Ohio, were the following:  -12 on Monday, -3 on Tuesday, -5 on Wednesday,  10 on Thursday, and  -10 on Friday.  What were the Mean and Median temperatures for the week?
a. Mean _____________
b. Median ____________
Evolutionary theories often emphasize that humans have adapted
Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking-even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed(individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25,27,25,23,25,26, and 25. Using the 5% level of significance, what should we conclude about the theory that 24 hours is the natural cycle?
a) Use the steps of the hypothesis ...
The average of three numbers
The average of three numbers is 20. If one of those numbers is 15...
Mean and standard deviation of house prices
Mean of $100,000 and a standard deviation of $35,000. What percentage of houses have prices between $90,000 and $130...
The mean amount of time that a manager spends
The mean amount of time that a manager spends in annual performance review with an employee is 27.2 minutes, with a standard deviation of 4.9 minutes. What percentage of the annual performance reviews in the department take between 22.3 and 32.1 minutes? Between 17.4 and 37 minutes? Between 12.5 and 41.9 ...
The median height of the 21 players
The median height of the 21 players on a girls' soccer team is 1.7 meters. What is the greatest possible number of girls who are less than 1...
25 employees were surveyed
25 employees were surveyed at AIU. 7 had less than 2 years, 11 had over 2 years and 7 had 5 years or more. What is the ...
Margo’s bank balances
Margo’s bank balances were:  $ -20 on Monday, $ 5 on Tuesday, $ 0 on Wednesday, $ - 14 on Thursday, and $ - 10 on Friday.  What were the Mean and Median Balances for the week?
a. Mean _____________
b. Median ____________
In a certain game each of the 5 players
In a certain game each of the 5 players recieved a score between 0 and 100 inclusive. If thier average score was 80...
In Prof. Smith`s management course
In Prof. Smith's management course the correlation between the students'  total score before the final examination and their final examination scores is r=.06. The pre-exam totals for all students in the class have mean 280 and standard deviation of 30. The final exams scores have mean of 75 and standard deviation of 8. Prof Smith lost Suee's final exam but knows that her total before the esam was 300...
The average age of 30 soldiers is 25
The average age of 30 soldiers is 25. The average age of first 15 of them is 24 and the last 14 of them is 26 ...
A telemarketer makes six phone calls per hour
A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two ...
Each of a sample of 184 residents
Each of a sample of 184 residents were asked how much they spent of lottery tickets. 124 responded with $0. The mean of the remaining was $20. The largest expenditure was $228...
By the year 2020, in a land far away
By the year 2020, in a land far away, the federal government requires car manufacturers to have a minimum of 30 miles per gallon (mpg) average over all the models it makes. Suppose that the GenYota company produces only five models with current mpg ratings of 21, 31, 22, 28, and 18. The manufacturer decides that it can only redesign the last of the models to meet the government requirement. What must the new mpg of this new fifth model be to meet the requirement for the five cars? (Round to the nearest mpg.)
A pair of dice are rolled
A pair of dice are rolled and their sum is ...
A softball league has ten teams
A softball league has ten teams in ...
A supplier of CD`s claims
A supplier of CD's claims that only 1% of disks are defective. In a random sample of 600 disks, it was found that 18 are defective. At 0.05 level of ...
A poll is conducted the day before a state election
A poll is conducted the day before a state election for senator. There are only two candidates and the poll shows that 53% of the oters surveyed favor the Green candidate, with a margin of 2.5 percentage points. Should the Green candidate plan a victory ...
Two dice are rolled
Two dice are rolled. It is agreed that if the sum is 7, John will be receiving $10; but for any other sum, John will have to pay out $2...
A sample of 900 homes sold recently
A sample of 900 homes sold recently in a state gave the mean price of the homes equal to $200,000. The standard deviation of the prices of all the homes in this state is $48,000. Construct a 99% confidence interval for the mean price of all homes in this state. (Any time you round, round to four decimal places.)
A university dean knows the age of students
A university dean knows the age of students at the school during the 1960s was normally distributed with a mean of 20.2 years and a standard deviation of 4.2 to determine if this demographic variable has substantially changed, a random sample of 36 current students is selected and the age recorded from each of them. For this sample the mean is 23.0. Is there significant difference in age between today students and those enrolled in the 1960? Test with an alpha of .05
Tioga Printers usually has 3 printing or typo error
Tioga Printers usually has 3 printing or typo error for every 100 pages when printing the first edition of a book. Becky has found 10 printing errors and 4 mathematical errors in the first edition of Ian Stewart's 287 page The Story of ...
I put 7 brown beans, 6 white beans
I put 7 brown beans, 6 white beans, 4 yellow peas and 3 green peas all into a container. What are the chances that I can pick out a green pea 4 times in a row. I will use a pair of tweezers so that I can't feel the shapes, and ...
Normal Distribution
for a specific year, american spent an average of $71.12 for books. Assume the variable is normally distributed.If the standard deviation of the amount spent on books is 8.42, find these probabliities for a normaly selected americans.
1. he or she spent more than $60 per year on books.

2...
Standard Score
a standard achievement test has a mean of 50 and a standard deviation of 10. (a) Find the probability that a student scores at least 55. (b) Find the percentage of scores that will fall between 47 and 57. (c) If the test is to be administered ...
Standard Deviation
a box contains 2 blue pins and 3 red pins, the color of a pin that is randomly chosen is recorded and the pin is returned to the box, given that this process is repeated 4 tomes and X is the number of times a blue pin is chosen, find the mean value and the standard deviation of X
variance
find the variance for 13, 1, 17, 11, 14,
Standard Score
On an auto mechanic aptitued test, the mean score is 270 points and the standard deviation is 35 points
a) if a students has a standardized score of 1.9...
Median
Karl has eight people in his family. he wondered how many hours of TV each of them might have watched in a week if the mean of the eight values were five ...
Normal Distribution
Population mean= 800 and standard deviation= 150; If you were to select a random sample of 500 students how many would you expect to have in your sample who spent $750 or less on clothing?
Normal Distribution
the mean yield a given year for sugar beets is 22 tons/acre and the standard deviation 3.8. For a sample of 280 fields, find the approximate number with a yield between 18.2 and 25.8. assume a normal distribution
Standard Deviation
At work Mr. Bussmann must wear a dress shirt, long pants, and shoes. He has four dress shirts(red, blue, orange, purple), three pairs of pants (green, yellow, tan) and two pair of shoes (...
Normal Distribution
1.  A normal distribution has a mean of 20 and a standard deviation of 4.  
a)  Find the percentile rank for a data value of 17 ( i....
Normal Distribution
the average age of lawyers is 40 years, with a standard deviation of 3 years. if a law firm employs 36 ...
Normal Distribution
the amount of daily deposits and daily withdrawals are given by independent random variables withnormal distributions.For deposits,the mean is $12000 and standard deviation of 4000.For withdrawals the mean is $10000 and standard deviation is $5000.Find the probablity that on any particular day the with drawal is greater than deposits
Statistics
Use a table of areas for the standard normal curve to find the required z-score.

Find the z-score for having area 0.09 to its right under the standard normal curve, that is, find z0.09
Standard Deviation
The amount of time required to assemble a component on a factory assembly line is normally distributed with a mean of 3.1 minutes nd a standard deviation of 0.6 minutes. Find the percentage of employees taht will take between 2.0 minutes and 2...
Standard Deviation
Assume that the length of time, x, between charges of a pocket calculator is normally distributed with a mean of 100 hours and a standard deviation of 15 ...
Standard Deviation
the neck size of men is normally distributed, with a mean of 15.5 inches for a shirt with a 0.5 inch standard deviation, and a new line of 1,000 shirts will be ...
Standard Deviation
A tire company tested another model of tire and found the tires to be normally distributed with respect to wear.  The average (mean)  tire wore  out at 46,000 miles, and the standard deviation was  24,000.  IF  2000 tires were tested, about how many are likely to wear out before 45...
Normal Distribution
an almanac reports the average person uses 118 gallons of water daily. If the standard deviation is 24 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 116 and 120 gallons. Assume the variable is normally distributed. Round your answe to two decimals
Standard Deviation
Find the standard deviation for this data set, correct to the nearest tenth.
45 39 26 52 34 30
Standard Deviation
Assume that the length of time, x, between charges of a pocket calculator is normally distributed with a mean of 100 hours and a standard deviation of 15 hours. Find the probability that the calculator will last between 80 and 120 hours between charges
Standard Deviation
2500 employess avg 15.5 years standard devitation 6.1 years how many with over 18 yrs
Standard Deviation
For a student to graduate, a high school requires that each student demonstrate competience in mathemantics by scoring 70 or above on a mathematics achievement test.  The scores of those students taking th test are normally distributed with a mean of 74 and a standard deviation of 4.8...
Standard Deviation
THE PROBAABILITY OF WINNING A VERTAIN LOTTERY IS 1/51, 949. FOR PEOPLE WHO PLAY 560 TIMES, FIND THE STANDARD DEVIATION FOR THE RANDOM VARIABLE  ...
Median
according to a census the median age of the 281421906 people surveyed is 35.3 years.  About how many people are older than 35...
Mean
331 students went on a field trip. Six buses were filled and 7 students traveled in ...
Average
Melody bought four boxes of Christmas ornaments.  Eaach box contained 12 ornaments.  There was an average of 2 broken ornaments per box.  3 of the boxes had 1 broken ornament ...
Mean
find the mean of the data
Statistics
A bag contains 5 black, 1 red, and 3 yellow jelly beans; you take 3 at ...
Statistics
A student takes a 20-question, true/false exam and on each question.Find the probability of passing if the lowest passing grade is 15 out of 20 .Would you consider this event likely to ...
Mean
A student of the author weighed a simple random sample of steak,s and the results are listed below.  The steaks are supposed to be 21 oz. beause they are listed on the mu as weight 20 oz. and the lose an ounce whne cooked. Use the listed weights  to find the mean. 17, 19, 21, 18, 20, 18, 19,20, 20, 21
Statistics
assume a sample of 1000 ...
Statistics
how many even 5 digit numbers can be formed from the numbers 1,2,4,7,8...
Statistics
The online access computer service industry is growing at an extraordinary rate. Current estimates suggest that only 20% of the home based computers have access to online services. The number is expected to grow rapidly in the next 5 years. Suppose 25 people with home-based computers were randomly and independantly sampled. Find the probabliity that fewer than 10 currently have access to online services
Statistics
A simple random sample of 40 salaries of NCAA football coaches has a mean of $415,953 and a standard deviation of $463,364...
Statistics
9. A data set consists of 72 test scores. Over a long period it has been found that the mean and standard deviation for these scores are known and that the scores are normally distributed. How many scores within this data set should lie within one standard deviation of the ...
Statistics
6 people are riding in car that has three seats in the front and three seats in the back.  If one person refuses to ride in the front and two people refuse to ride in the ...
Statistics
300 beans twice as many white than black how many black are there
Statistics
A RANDOM SAMPLE OF 25 BOOKS HAS A VARINACE OF 81 PAGES. fIND THE 95% CONFIDENCE INTERVAL OF THE TRUE POPULATION VARIANCE
Statistics
The online access computer service industry is growing at an extraordinary rate. Current estimates suggest that only 20% of the home based computers have access to online services. The number is expected to grow rapidly in the next 5 years. Suppose 25 people with home-based computers were randomly and independent sampled. Find the probability that fewer than 10 currently have access to online services
Statistics
Antonio measures the alcohol content of whiskey for his Chemistry 101 lab. He actually measures the mass of 5.8 milliliters of whiskey -- a chemical calculation then finds the percent alcohol from the mass. The standard deviation of students' measurements of mass is σ = 10.6 milligrams (mg). Antonio repeats the measurement 8 times and records the mean x of his 8 measuremen
(b) How many times must Antonio repeat the measurement to reduce the standard deviation of x to 3.75 ...
Statistics
Suppose the variance = 289...
Statistics
1. Professor Kline has 125 students in his Western Civilization Class.  At the end of the semester, the average final grade was µ = 68.85 and a standard deviation σ = 7.25.  
How many students received a final score:
a. better than 90?
b. between 70 and 85?
c. less than 60.50?
...
Statistics
The mean on this test is 3.5 with a standard deviation of .5.  1. Sally scores 1.5 on this ...
Statistics
An automobile manufacturer has three factories, A, B, C.  They produce 50, 30, and 20%, respectively, of a specific model of car.  30% of the cards produced in the factory A are white, 40% of those produced in factory B are white, and 25% produced in factory C are white.  If an automobile produced by the company is selected at ...
Statistics
If a student has a standardized score of 1.9, how many points is thatWITH THE MEAN =264 AND ST=40
Statistics
find the average time to clean the class rooms on the campus; the duties are emptying trash, wipe desks, vacuum, clean boards, and straighten desks
Statistics
The number of eggs a female house fly lays during her lifetime is normally distributed, with a mean of 800 eggs and a standard deviation of 100 eggs. Random sample of size 15 are drawn from this population and the mean of each sample is ...
Statistics
Antonio measures the alcohol content of whiskey for his Chemistry 101 lab. He actually measures the mass of 5.8 milliliters of whiskey -- a chemical calculation then finds the percent alcohol from the mass. The standard deviation of students\' measurements of mass is σ = 10.6 milligrams (mg). Antonio repeats the measurement 8 times and records the mean x of his 8 measuremen
(b) How many times must Antonio repeat the measurement to reduce the standard deviation of x to 3.75 ...
Statistics
find the probability that a student will score between 82 and 88 on a test
Statistics
Mean of 440 seconds and a standard deviation of 60 ...
Statistics
How many different ways can five managers be seated a round table?
Statistics
how many different combinations can you make 41 cents out of quarters, ...
Statistics
in a testing a new rug, researchers found that 5% of all patients using it will have amild side effect. A random sample of 15 patients using the drug is ...
Statistics
The average gas mileage of a certain model car is 28 miles per gallon If the gas mileages are normally distributed with a standard deviation of 1...
Statistics
The scores of a test have a mean of 100 and a standard deviation of 15. if a personal manager wishes to select from the top 75% of applicants who take the test, find the cutoff ...
Statistics
How many ways can you select 3 member group out of 15 people?
Statistics
find the iq score separating the top 35% from the others

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This Probability and Statistics page lists word problems on statistics topic.