Question

Suppose a simple random sample of size n =13 is obtained from a population with μ= 68 and σ =16.

​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample​ mean? Assuming the normal model can be​ used, describe the sampling distribution x.

​(b) Assuming the normal model can be​ used, determine ​P(x < 72.2 ).

​(c) Assuming the normal model can be​ used, determine ​P(x ≥ 69.2).

Answer 1

This is a normal distribution question with

Sample size (n) = 13

a) Since we know that

b) P(x < 72.2)=?

The z-score at x = 72.2 is,

z = 0.9465

This implies that

c) P(x > 69.2)=?

The z-score at x = 69.2 is,

z = 0.2704

This implies that

P(x > 69.2) = P(z > 0.2704) = 1 - 0.6065737299500419

PS: you have to refer z score table to find the final probabilities.

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