Given a normal population with a mean of 6.5 and standard deviation of 1.3 years

Question

Given a normal population with a mean of 6.5 and standard deviation of 1.3 years. A random sample of 3 is obtained. (a). The mean of the sampling distribution of the sample mean is (b). The standard error of the sampling distribution of the sample mean is Round your answer to four decimal places. (c). Use the standard normal tables to find the ninth percentile of the standard normal distribution Use the closest z value. (d), 9% of the time the sample mean will be less than what value? Round your answer to two decimal places. (Hint: use your answers from parts (a) to (c))

Explanation / Answer

A) mean of sampling distribution = mean of population = 6.5

B) Standard error = standard deviation /sqrt (n) = 1.3/sqrt (3) = 0.7506

C) ninth percentile = - 1.34

D) Z = (X - mean) /Standard deviation,

Here Standard deviation is 0.7506

X = 6.5 - 1.34 * 0.7506 = 5.49

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