Probability question

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16 inches, and standard deviation of 1.9 inches.

a. If one item is chosen at random, what is the probability that it is less than 21 inches long?

b. If one item is chosen at random, what is the probability that it is greater than 19 inches long?

c. If one item is chosen at random, what is the probability that it is between 15 and 21 inches long?

Answer 1

You can use CDF tables to find answers to these. Let x represent the length of the object.

a) P(x < 21) = CDF(21) = 0.9958

b) P(x > 19) = 1 - P(x < 19) = 0.0572

c) P(x < 21) - P(x < 15) = 0.9958 - 0.2993 = 0.6965