Need Help As Soon As Possible- A manufacturer knows that their items have a normally distributed lifespan, with a mean of...

Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.8 years, and standard deviation of 3.4 years.

If you randomly purchase 20 items, what is the probability that their mean life will be longer than 11 years? (Give answer to 4 decimal places.)

Answer 1

Standardize the normal random variable.

z = (x - µ) / (σ / √n)

z = (11 - 10.8) / (3.4 / √20)

z = 0.26

Using our z-table, a z-score of 0.26 gives us a probability of .6026

The questions asks for the probability the mean life will be longer than 11 years. Which means we want the probability to the right of this z-score, so we need to subtract from 1.

1 - .6026 = .3974 or 39.74%