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Question

A manufacturer knows that their items have a normally distributed length, with a mean of 16.8 inches, and standard deviation of 1 inches.

If one item is chosen at random, what is the probability that it is less than 19.6 inches long? (Give answer to 4 decimal places.)

Answer 1

Begin by standardizing the normal random variable

z = x - mean / st, dev

z = 19.6 - 16.8 / 1

z = 2.8

The probability associated with a z-score of 2.8 is 0.9974.

The question asks for the probability that a randomly chosen item is less than 19.6 inches long. It is asking for the area less than a z-score of 2.8, which is 0.9974.