A random sample of size 33 is to be selected from a population that has a mean 𝜇 = 48 and a standard deviation 𝜎 of 13.

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A random sample of size 33 is to be selected from apopulation that has a mean 𝜇 = 48 and astandard deviation 𝜎 of 13.(a) Find the mean of this sampling distribution. (Give your answercorrect to nearest whole number.)(b) Find the standard error of this sampling distribution. (Giveyour answer correct to two decimal places.)(c) What is the probability that this sample mean will bebetween 45 and 55? (Give your answer correct to fourdecimal places.)(d) What is the probability that the sample mean will have a valuegreater than 48? (Give your answer correct to four decimalplaces.)(e) What is the probability that the sample mean will bewithin 3 units of the mean? (Give your answer correct tofour decimal places.)