1) Consider an investigator is testing to see if different locations are contaminated with a certain toxin. Suppose the probability of a location being contaminated is 0.2, and that the investigator collects a sample at 15 different locations. Assume the locations are far enough away from each other to be independent. a) For this experiment, what is the mean and standard deviation of the number of locations that were contaminated? b) What is the probability they will find at least 1 contaminated location? c) What is the probability they will find at most 3 contaminated locations? d) Using R, produce a plot of this probability distribution.

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Answered: 1) Consider an investigator is testing…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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9. Women's heights are normally distributed with a mean of 63.8 in and standard deviation of 2.6 in. a) If one woman is randomly selected, find the probability that her height is less than 62.4 inches. b) If one woman is randomly selected, find the probability that her height is more than 64.5 inches. c) If one woman is randomly selected, find the probability that her height is between 61.0 inches and 68.0 inches. d) If 24 women are randomly selected, find the probability their mean height is less than 62.1 inches. e) Find P17.
Women have pulse rates that are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. a.) What is the probability that a woman has a pulse rate higher than 73.2 beats per minute? b.) What pulse rate would separate the lowest 65% of women from the top 35%? c.) What is the probability that a group of 15 women has a mean pulse rate between 74.1 and 83.5 beats per minute? d.) Even though the sample size is less than thirty in part (c) of this question, why can the Central Limit Theorem still be applied? e.) If you were a doctor who is selecting pulse rates as cutoff values for determining whether further tests are needed for patients, which result is more relevant to use, part (a) or part (c)? Why?
1.A personnel manager is employed in a corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.Find the 95th percentile for the mean time to complete one month's reviews. (a) Sketch the graph.(b) Give the 95th Percentile. (Round your answer to two decimal places.)
3. An article by S. M. Berry titled “Drive for Show and Putt for Dough (Chance, Vol 12(4), pg 50-54)” discussed driving distances of PGA players. The mean distance for tee shots on the 1999 men’s PGA tour is 272.2 yards with a standard deviation of 8.12 yards. Assuming that the 1999 tee-shot distances are normally distributed, find the percentage of such tee shots that went a. between 260 and 280 yards. b. more than 300 yards. 4. Do Exercise 6.103 on page 288 in the textbook. Show work. (image attached) 5. Refer to question 3 in this homework. The article “Drive for Show and Putt for Dough (Chance, Vol 12(4), pg 50-54)” discussed driving distances of PGA players. The mean distance for tee shots on the 1999 men’s PGA tour is 272.2 yards with a standard deviation of 8.12 yards. Assuming that the 1999 tee-shot distances are normally distributed answer the following questions: a. Determine the quartiles of the driving distances b. Find the 95th percentile. c. Obtain the third decile (i.e.…
11. Suppose Google creates a new workspace in Toronto. The building operates with 1,200 computers. On average. about 50 are out of service. During a trial run for opinions on new computer software, a sample presentation is given to 25 people in a room with 28 computers, determine; a) The mean and standard deviation of a normal approximation of working computers b) The probability that there will be at least 25 working computers in the room.
4. The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations. What's the approximate probability that the average price for 16 gas stations is over $4.69? а. b. Find the probability that the average price for 30 gas stations is less than $4.55. C. Sketch graphs for a and b
5) The daily revenue at a university snack bar has records to indicate that the mean daily revenue is $2,400 and standard deviation is $600. A random sample of 81 days was selected. Find the approximate probability that the average revenue for the sample is less than $2,300.
Q)In a certain large university, students spend on average $75 a month on pizza, with a standard deviation of $24.30.A marketing specialist plans to survey 225 students, and ask them to record how much they spent on pizza during April.(a) What would be the standard deviation of the sample mean?(b) What is the probability that the researcher will get a sample mean less than $72.5?
The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.3 grams with a standard deviation of 0.2 grams. a) What is the probability that a randomly chosen mouse has a mass of less than 20.16 grams? b) What is the probability that a randomly chosen mouse has a mass of more than 20.51 grams? c) What proportion of mice have a mass between 20.14 and 20.39 grams?
3. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.Find the 95th percentile for the mean time to complete one month's reviews.
2. The number of shots on goal in an amateur hockey league's games is normally distributed, with a mean of 56.3 and a standard deviation of 8.1 shots. a) In what percent of the games will there be fewer than 40 shots on goal? b) In what percent of the games will there be between 50 and 60 shots on goal? c) What is the probability that a game will have more than 66 shots?
5. The ages of U.S. commercial aircraft have a mean of 13 years and a standard deviation of 7.9 years (based on data from Aviation Data Services). a. If the Federal Aviation Administration randomly selects 35 commercial aircraft for special stress tests, find the probability that the mean age of this sample group is greater than 15 years? b. If the Federal Aviation Administration randomly selects 42 commercial aircraft for special stress tests, what is the mean sample age of the aircraft for the top 75% of the sample?4

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