QUESTION 1

1) The weight of competition pumpkins at the Circleville Pumpkin Show in Circleville, Ohio, can be represented by a normal distribution with a mean of 703 pounds and a standard deviation of 347 pounds.

a. Find the probability that a randomly selected pumpkin weighs at least 1,622 pounds.(2 Marks) b. Find the probability that a randomly selected pumpkin weighs between 465.1 and 1,622 pounds.(4 Marks)

2) Customers arrive at a drive-through teller window of a bank. They stay in line when the teller is busy. The service time is exponentially distributed with a mean of four minutes.

a. What is the probability that the next customer in line will take longer than seven minutes to be served?(2 Marks) b. What is the probability that the next customer in line will take less than eight minutes to be served?(2 Marks) c. What is the probability that the next customer in line will take between three and six minutes to be served?(4 Marks)

TOTAL: 14 MARKS

QUESTION 2

1) A Family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them than the last 26 houses that sol in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days.

a. What assumption regarding the population is necessary for making an interval estimate for the population mean?(2 Marks) b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood.(4 Marks)

2) A random sample of eight drugstores shows the following prices (in $ of a popular pain reliever:

3.50 4.00 2.00 3.00 2.50 3.50 2.50 3.00a. What is the standard deviation for the sample?(2 Marks) b. Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean.(4 Marks)

TOTAL: 12 MARKS