Question

A manufacturer knows that their items have a normally distributed length, with a mean of 13.3 inches, and standard deviation of 3.6 inches.

If one item is chosen at random, what is the probability that it is less than 21.4 inches long?

Answer 1

Mean = $\mu$ = 13.3

Standard deviation = $\sigma$ = 3.6

We have to find P(X < 21.4)

For finding this probability we have to find z score.

$z =\frac{x-\mu}{\sigma} =\frac{21.4-13.3}{3.6}=2.25$

That is we have to find P(Z < 2.25)

P(Z < 2.25) = 0.9878    ( Using z table)