A random sample of size n 78 is taken from a population wit

A random sample of size n = 78 is taken from a population with mean ? = ?14.8 and standard deviation ? = 3.

What is the probability that the sample mean falls between ?15 and ?14? (Do not round intermediate calculations. Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Solution

So the probability that the sample mean falls between ?15 and ?14 is

P(-15<xbar<-14)

= P((-15+14.8)/(3/sqrt(78)) <(xbar-mean)/(s/vn) <(-14+14.8)/(3/sqrt(78)))

=P(-0.59<Z<2.36) =0.7133 (from standard normal table)