The population mean and standard deviation are given below. Find the required pr

Question

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= 75, find the probability of a sample mean being greater than 217 if = 216 and =62. For a sample of n 75, the probability of a sample mean being greater than 217 if = 216 and = 6.2 is (Round to four decimal places as needed.) Would the given sample mean be considered unusual? The sample mean be considered unusual because it within the range of a usual event, namely within | of the mean of the sample means.

Explanation / Answer

Given: µ = 216, = 6.2

n = 72, To calculate P( X > a) = 1 - P (X < a), as the normal tables give us the left tailed probability only.

For P( X < a)

Z = (217 – 216)/[6.2/75] = 1.4

The probability for P(X < a) from the normal distribution tables is = 0.9188

Therefore the required probability = 1 – 0.9188 = 0.0812

The sample mean cannot/can't be considered unusual because it lies/falls within the range of a usual event, namely within 95% of the mean of sample means.

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