Question

The weight of the contents of a type of box of cereal is normally distributed with population mean μ = 30 ounces and population standard deviation σ = 3.2 ounces. A random sample (size n = 25) is taken. What is the probability that the sample mean is less than 31.74 ounces?

Answer 1

given

μ = 30 ounces

σ = 3.2 ounces.

n=25

the probability that the sample mean less than 31.4

p(xbar<31.4)=p(x-μ/ σ/sqr(n) < 31.4-30/3.2/sqr(25))

=p(z<1.4/3.2/5)

=p(z<1.4/0.64)

=p(z<2.1875)

from table

=0.9857