Suppose a simple random sample of size n equals=37 is obtained from a population

Question

Suppose a simple random sample of size n equals=37 is obtained from a population with equals=68 and =14.

(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 over x

(b) Assuming the normal model can be used, determine P(x over x < 71.6).

(c) Assuming the normal model can be used, determine P(x over x > over slash 70.4)

Explanation / Answer

a ans) sampling distribution of x is approximately normal is true

b ans) p(x<71.6) =[71.6-68]/14=0.257

from standard z table the value of 0.257 is .5987

c ) p(x>70.4) =[70.4-68]/14=0.1714

from standard z table we have 1-0.5675=0.4325

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