A manufacturer knows that

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 15.5 inches, and standard deviation of 1.7 inches.

If one item is chosen at random, what is the probability that it is less than 13.9 inches long?

Answer 1

Prob ( x < 13.9)

= Prob ( x < (13.9-15.5)/1.7) =

Prob( z < -0.94117640588...) = 0.173609..

17.3609%

Answer 2

Since we know the items have a normally distributed length, we can get the Z score which will determine how many standard deviations from the mean that 13.9 inches is. From there, we can use a table for the standard normal distribution to get the probability.

Z = (x - mean)/standard deviation

Z = (13.9 - 15.5)/1.7

Z = -1.6/1.7

Z = -0.94

Now use the table for standard normal distribution and find the area to the left of Z = -0.94.

http://www.z-table.com/

The answer is 0.1736