2. ABC Bicycle Shop in Ottawa sells mountain bikes and offers a maintenanceprogram to its customers. The manager has found the repair bill during the mainte-nance program's first year to follow a distribution with mean $15.30 and standarddeviation $7.00.(a) What is the probability a random sample of 40 customers will have amean repair cost exceeding $16.00?(b) What is the probability the mean repair cost for a sample of 100 gus-tomers, will be between $15.10 and $15.80?(c) The manager has decided to offer a spring special. He is aware of themean and standard deviation for repair bills last year. Therefore, he has decidedto randomly select and repair the first 50 bicycles for $14.00 each. Since this isa risky thing to do, the manager wants to know the probability that the springspecial offer would lead him to have a net loss. Please calculate the probabilityfor him.

Answered: 2. ABC Bicycle Shop in Ottawa sells…

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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1.a.The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean ? = $633 and standard deviation ? = $46. If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.) b.A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.2 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (Round your answer…
Assuming that student incomes from employment in industry during the day are normally distributed with a mean income of $30,000 and a standard deviation of $3,000. a) What is the probability that a randomly selected student earns more than $30,000? b) What’s the probability that a randomly selected student earns between $27,000 and $33,000? c) What’s the probability that the average income of a sample of 30 students is less than $28000?
The manager of the local Walmart Supercenter is studying the number of items purchased by customers in the evening hours. Listed below is the number of items for a sample of 30 customers. 9 12 5 8 4 6 6 7 11 9 8 14 9 12 5 4 10 6 18 10 6 10 11 5 What is the mean number of items? What is the median number of items? What is the range of number of items? What is the standard deviation? About 95% of the number of items are between what two values? Lower limit 10 9 13 12 13 5 Organize the number of items into a frequency distribution. What is the lower limit of the second class? What is the mean of the data organized into a frequency distribution? What is the standard deviation of the data organized into a frequency distribution? Compare these values with those computed in parts (A) and (D). Why are they different? Upper limit
7. Salaries for newly graduated college seniors is normally distributed with a mean of $42,500 per year. The standard deviation is $5800. Write an expression that describes the probability of a randomly-selected college graduate earning over $36,700. Then fill in the missing values under the normal curve, and use the empirical rule to find this probability. 34% 34% 13.5% 13.5% 2.35% 2.35% H-30 H-20 H+2o H+30
3. A business school claims that students who complete a three month course of typing course can type on average, at least 1200 words an hour. A random sample of 25 students who completed this course typed, on average, 1130 words an hour with a standard deviation of 85 words. Assume that the typing speeds for all students who complete this course have an approximate normal distribution. Using the 5% significance level, can you conclude that the claim of the business school is true?
10. In a study conducted to determine the role that sleep disorders play in academic performance, researcher Jane Gaultney conducted a survey of 503 randomly selected students with a known sleep disorder (such as narcolepsy, insomnia, or restless leg syndrome) and found their mean GPA was 2.65 with a standard deviation of 0.87. Similarly, she randomly selected 1342 students with no known sleep disorders, and found their mean GPA to be 2.82 with a standard deviation of 0.83. You may assume that both population GPA's are normally distributed. Use a significance level of 0.05 to test whether the two groups have different mean GPA's. As a follow-up, construct and interpret a 95% confidence interval for the true difference in the mean GPA's of the two groups. What would be the type I and type II errors for this problem?
4. According to a 2019 Federal Reserve report, 54% of U.S. young adults who went to college took on some debt for their education. Suppose we take a random sample of 400 U.S. young adults who went to college and took on some debt, a) Find the mean and standard of the sampling distribution of ?̂. mean= ?? = standard deviation of the sample proportion, ?? = b) Determine the probability that more than 60% of the persons in the sample took on some debt.
4. TomTom, the producer of GPS devices, reported that the fastest drivers in the nation are in Mississippi. In Mississippi, interstate drivers average 70.1 miles per hour. Assume that the speed of cars traveling on Mississippi’s interstates follows the normal distribution with a standard deviation of 7.2 miles per hour. a. What is the probability that a randomly selected car on a Mississippi interstate is traveling 1. faster than 65 miles per hour? 2. slower than 72 miles per hour? 3. between 60 and 66 miles per hour? 4. between 78 and 85 miles per hour? b. Confirm the answers to part a with Excel. c. What average speed should I drive if I want to travel faster than 70% of the cars on the interstate?
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.…
A. The salaries of pharmacy techs are normally distributed with a mean of $33,000 and a standard deviation of $4,000. If a pharmacy tech is selected at random, what is the probability they make more than $38,000? The answer should be typed as a decimal with 4 decimal places. B. The salaries of pharmacy techs are normally distributed with a mean of $33,000 and a standard deviation of $4,000. What is the minimum salary to be considered the top 6%? Round final answer to the nearest whole number. C. The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places.
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
. The on-campus housing costs for a semester at a state university are Normally distributed with a mean of $1553 and a standard deviation of $329.(a) What is the distribution of the mean on-campus housing cost for a semester at this university for a random sample of 50 students? (b) What is the probability that a randomly selected on-campus student spends more than $1200 per semester? (c) What is the probability that a random sample of 50 students spends an average of less than $1500? (d) What is the probability that a random sample of 50 students spends an average of $1450 to $1600 per semester?

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