Question

(a)
The number of years before a Sunshine CD player breaks down is normally distributed with a mean of 4.1 years and a standard deviation of 1.3 years.



Part A

Which of the graphs below represents the situation?

A


B


C


D


(b)
Part B

Find the probability that a CD player breaks down in less than 3 years. Explain the steps you took to find your answer.

Math


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Answer 1

(a) Pick the graph that shows a normal bell curve centered at 4.1 (the peak at 4.1) with the area to the left of x = 3 shaded. (In other words, the curve must be centered at 4.1 and the region x < 3 is shaded.)

(b) Let X ~ N(4.1, 1.3^2). We want P(X < 3).

1. Standardize: z = (3 − 4.1)/1.3 = −1.1/1.3 ≈ −0.846.
2. Use the standard normal distribution: P(Z < −0.846) ≈ 0.199 (≈0.20).

So the probability a CD player breaks down in less than 3 years is about 0.199 (≈19.9%).