The gamma function of ( x + 4 ) in term of gamma function of x ,

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Chapter A, Problem 15E

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To find: The gamma function of (x+4) in term of gamma function of x,

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Please help me organize the proof of the following theorem:

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n = 65, find the probability of a sample mean being greater than 225 if μ = 224 and σ = 3.5. For a sample of n = 65, the probability of a sample mean being greater than 225 if μ=224 and σ = 3.5 is 0.0102 (Round to four decimal places as needed.)