A certain population has a mean of 463 and a standard deviation of 38. Many samp

Question

A certain population has a mean of 463 and a standard deviation of 38. Many samples of size 55 are randomly selected and the means calculated.

(a) What value would you expect to find for the mean of all these sample means? (Give your answer correct to nearest whole number.)

(b) What value would you expect to find for the standard deviation of all these sample means? (Give your answer correct to two decimal places.)

(c) What shape would you expect the distribution of all these sample means to have?

skewed right

approximately normal

skewed left

uniform

Explanation / Answer

a. As per central limit theorem mean of the sample mean =463

b. Again as per central limit theorem standard deviation =sd/sqrt(n)=36/sqrt(55)=4.85

C. As per central limit theorem for sample of size>30, distribution is approximately normal.

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