5. The distribution of heights of a certain brecd of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimeters. Assume the distributions of both typcs of breeds are normally distributed. (a) Suppose we are taking a random sample of 64 terricrs. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 64 terriers excceds 75 centimcters. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers exceeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.

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