STATS Final Homework Assignment 2015

| February 14, 2018

1. An experiment was performed on a certain metal to determine if the strengthis a function of heating time. Results based on 15 metal sheets are givenbelow. Use the simple linear regression model.X =30X2=100Y = 45Y2 =165XY =120Find the slope and intercept and write the estimated Regression equation.Find SSE, SST, and SSR. Also find the Coefficient of Determination andinterpret it. Find the correlation coefficient.2. The diameter of small Nerf balls manufactured at a factory in China isexpected to be approximately normally distributed with a mean of 5.2 inchesand a standard deviation of .08 inches. Suppose a random sample of 20 ballsare selected. What percentage of sample means will be less than 5.15inches?3. Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2of which are defective. One item is drawn from each container: What is theprobability that one of the items is defective? (Hint: you have to use both ruleof addition and rule of multiplication/conditional probability rules)4. Joe is considering pursuing an MBA degree. He has applied to two differentuniversities. The acceptance rate for applicants with similar qualifications is25% for University A and 40% for University B. What is the probability that Joewill be accepted at one and only one university?5.An important part of the customer service responsibilities of a cablecompany relates to the speed with which trouble in service can be repaired.Historically, the data show that the likelihood is 0.75 that troubles in aresidential service can be repaired on the same day. For the first five troublesreported on a given day, what is the probability that: Fewer than two troubleswill be repaired on the same day?6. The College Student Journal (December 1992) investigated differences intraditional and nontraditional students, where nontraditional students aredefined as 25 years or older and working. Based on the study results, we canassume the population mean and standard deviation for the GPA ofnontraditional students is ยต=3.5 and =0.5. Suppose a random sample of 100nontraditional students is selected and each student’s GPA is calculated.What is the probability that the random sample of 100 nontraditionalstudents have a mean GPA greater than 3.65?7. Suppose that the waiting time for a license plate renewal at a local office of astate motor vehicle department has been found to be normally distributedwith a mean of 30 minutes and a standard deviation of 8 minutes. What is theprobability that a randomly selected individual will have a waiting timebetween 15 and 45 minutes.

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