Question

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.35 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.36 inches? Enter your answer as a percentage rounded to two decimal places.

Answer 1

15.87%

Explanation:

Notice that the mean of 0.35 inches with a standard deviation of 0.01 gives you when you add (to the right of the distribution), exactly 0.36. Since you want to find the probability (or percentage) of the bolts that have diameter LARGER than 0.36 in, that means you want to estimate the area under the Normal distribution curve from 0.36 to the right). See attached image.

We can use the tables of Z distribution for that, or the standard normal tables:

P(x>0.36) = P(z>(0.36-0.35)/0.01) = P(Z>1) = 0.1587 = 15.87%