Hi,

A "random sample of size n = 25"  is chosen from a normal population with known mean, m=8, and s.d., s = 4 

The idea is:, the m = 8 is used for 'comparative' purposes and 

4/sqrt(25) = 4/5 is the adjusted s.d. AND for m < 7  ⇒ z =  (7-8)/(4/5) = -1.25 

which gives us:

P(m < 7) = P(z< -1.25) =NORMSDIST(-1.25)  = .1057

For sample mean < 9 ⇒ z =  (9-8)/(4/5) = 1.25    and   NORMSDIST(1.25)= .8944

P(sample mean between 7 and 9) = NORMSDIST(1.25) - NORMSDIST(-1.25)

                               = .8944 - .1057

 

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