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Question 3 (a) An orange juice producer buys oranges from a large orange grove that has one variety of oranges. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounces. Suppose that you select a sample of 25 oranges. (i) What is the probability that the sample mean amount of juice will be at least 4.60 ounces? (4 marks) Seventy-seven percent of the sample mean amount of juice will be greater than what value of ounces? (5 marks) (b) A marketing researcher wants to estimate the mean amount spent ($) on Amazon.com by Amazon prime member shoppers, Suppose a random sample of 100 Amazon Prime member shoppers who recently same a purchase on Amazon.com yielded a mean of $1,500 and a standard deviation of $200. (i) Construct a 95% confidence interval estimate for the mean spending for all Amazon Prime member shoppers. (5 marks) (in) Interpret the interval constructed in (i). (2 marks) (c) A bottle water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company specifications that the standard deviation of the amount of water per bottle is Coga gallon. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle is 0.995 gallon. Is there evidence that the mean amount is different from 1.0 gallon? ( Use a = 0.01). (9 marks) [Total : 25 Marks]