ADVANCED PROBABILITY AND STATISTICS (JOINTS)

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ADVANCED PROBABILITY AND STATISTICS (JOINTS)
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The operation manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among three daily shifts. She randomly selects 427 recently made shirts and carefully inspects them. Do these data provide sufficient evidence to infer that there is a relationship between quality and the three shifts? Use 1% significance level. ShiftShirt condition 1...
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To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3700, and the average first-year commission for each new account opened is $5300. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.Assume that the number of new accounts you get randomly is:Simulation TrialNew Accounts102030405062728191100111122131142150160170180191200211220231240250Construct a spreadsheet...
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A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 499 seconds to run the mile.

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(37 marks) Your client is planning to invest some money with your investment company. The client narrows their options down to 2 investment strategies X and Y , and from past experience the annual percentage returns are as follows: X ∼ N(3, 1 2 ) and Y ∼ N(5, 3 2 ). (a) For each investment strategy, calculate the probability of a negative return. [4 marks] (b) For each investment strategy, calculate the probability of return greater than 5.5%.
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The current Men’s high school track record for the mile is 3:53, set by Alan Webb back in 2006. The average mile time for a high school senior is 4:22 (262 seconds), with a standard deviation of 6.3 seconds. Paul, a high school senior, runs the mile in 4:19 (259 seconds). 1.) What is Paul’s percentile ranking among high school seniors? HINT: don’t forget that in this case less is better so you will need to reverse the scale!2.) If Brian’s...
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A research engineer for a tire manufacturer is investigating tire life for a new rubber compound. He has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss...