Answer:
We know that Z score is given by,
Where is the sample mean
is the population mean
is the population standard deviation and n is sample size.
(a) Given, , , and n=25
Thus the probability that the sample mean is great than 60, i.e.
We get,
And from Z table we get that the probability of is 0.7791.
(b) When sample mean is less than 57:
And from Z table we get that the probability of is 0.3503.
(c) When sample mean between 57 and 60:
From the above calculation, and
Thus,
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