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Question 5 (12 marks) Marks a. A survey nds that a shopper spends, on average, 35 minutes in a store with a standard deviation of 8.3 minutes. Assume a normal distribution. i. Find the probability that a customer spends less than 28 minutes in a store. [2] ii. Find the probability that a customer spends more than 41 minutes in a store. [2] iii. If 10 customers are randomly selected, what is the probability that the mean time spent by customers in a store is between 28 and 41 minutes? [2] Question 5 (continued) Marks b. Suppose that a university is interested in estimating the yearly income for a person with a bachelor's degree. Thirty people with a bachelor's degree are randomly selected. Assume that the average yearly income is normally distributed. It is found that the average yearly income of 30 people is $65,000 with a sample standard deviation of $20,000. i. State the point estimate of the average yearly income of a person with a bachelor's degree. [1] ii. Construct a 95% condence interval for the average yearly income of a person with a bachelor's degree. [3] c. If a quality control manager wants to estimate the mean lifespan of light bulbs :30 hours with 90% condence, how many sample light bulbs are needed? Assume the population standard deviation is 120 hours. [2]