Question

A manufacturer knows that their items have a normally distributed length, with a mean of 20 inches, and standard deviation of 5 inches.

If one item is chosen at random, what is the probability that it is less than 13.7 inches long? (Give answer to 4 decimal places.)

Answer 1

Solution :

Let X be a random variable which represents the length of items produced.

Given that, X ~ N(20, 5²)

Mean (μ) = 20 inches

SD (σ) = 5 inches

We have to find P(X < 13.7 inches).

We know that, if X ~ N(μ, σ²) then

Using "pnorm" function of R we get, P(Z < -1.26) = 0.1038

If one item is chosen at random, the probability that it is less than 13.7 inches long is 0.1038.

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