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