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Question: the number of mampm candies in a single bag weighing...

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The number of M&M candies in a single bag weighing 8 oz follows some unknown distribution with a mean of 210 candies and variance of 16 candies. Assume that number of M&M in a single bag weighing 8 oz are iid random variables. Using this information answer the following.

(a) Find the approximate probability distribution of average no. of M&M candies in 36 bags weighing 8 oz each. (Name the distribution and identify the parameters)

(b) Can you find the probability that number of candies in a single bag weighing 8 oz will be more than 220 candies? If yes compute it else explain why not?

(c) Can you find the probability that average number of candies in 36 bags weighing 8 oz each will be more than 211 candies? If yes compute it else explain why not?

(d) A random sample of 36 M&M bags weighing 8 oz each was collected. The mean and standard deviation of the number of M&M candies in those 36 bags was found to be 212 and 10 respectively. Using this information, construct a two sided 95% CI for the true mean number of candies M&M candies in a 8 oz bag.

(e) Interpret the above Confidence Interval within the context of the problem.

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