Question 850750: 1. A random sample of size n = 25 is chosen from a normal population with known mean, m=8, and s.d., s = 4.
I know the sampling distribution of the sample mean is .8 but I don't understand this question:
Determine the probability of having a sample mean less than 7.
or
having a sample mean between 7 and 9.
I just need to figure out how to do this because I can't figure it out, if you could explain it to me!
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
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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