Statistics Chapter 7 Homework

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.4 years, and a standard deviation of 1 year.

If you randomly purchase 3 items, what is the probability that their mean life will be longer than 3 years? (Give answer to 4 decimal places.)

Answer 1

Compute z-stat

z-stat = (sample mean - population mean)/(population standard deviation/sqrt(sample size)

z-stat = (3 - 3.4)/(1/sqrt(3))

then find P(z > z-stat) = P(z < -z-stat) from standard normal probability table