Question

Suppose a random sample of n = 25 observations is selected from a normal population,
with mean 106 and standard deviation 12.
mean=106 sd = 12/sqroot25=2.4
B.Find the probability that the sample mean deviates from the population mean
= 106 by no more than 4.
C.Sketch the probability distribution from part B, showing the area that
represents the probability you found.
I don't really understand these problems any help would be appreciated. :D

Answer 1

B. The required probability is expressed as:
\[\large P(\frac{102-106}{2.4}<Z <\frac{110-106}{2.4})\]
which reduces to:
\[\large P(-1.67<Z <1.67)\]