A manufacturer knows that their items have a normally distributed length, with a mean of 8.8 inches, and standard deviation of 0.7 inches. If one item is chosen at random, what is the probability that it is less than 8.2 inches long?

0.1949

Step-by-step explanation:

Given a normal distribution with;

Mean(m) = 8.8 inches

Standard deviation (sd) = 0.7 inches

If one item is chosen at random, what is the probability that it is less than 8.2 inches long?

Find the Z-score :

x = 8.2 inches

Z = (x - m) / sd

Zscore = (8.2 - 8.8) / 0.7

Zscore = - 0.6 / 0.7

Zscore = - 0.857 = - 0.86

P(Z < - 0.86) :

From z distribution table :

P(Z < - 0.86) = 0.1949

If one item is chosen at random, there is a probability of 0.1949 that it will be less than 8.2 inches long.