Suppose a random sample of n 16 observations is selected fr

Suppose a random sample of n = 16 observations is selected from a population that is normally distributed with mean equal to 109 and standard deviation equal to 11.

(a) Give the mean and the standard deviation of the sampling distribution of the sample mean x.

(b) Find the probability that x exceeds 114.

(c) Find the probability that the sample mean deviates from the population mean ? = 109 by no more than 3.

Solution

Mean of sample=109

std dev of sample=11/rt16 = 2.75

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b) P(X>114) = P(Z>1.82) =0.4656

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c) P(dev is <3) = P(|X-109|<3)

= P(Z<3/2.75) = 0.1611*2 =0.3222