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

Answer 1

(a) The correct graph is the bell (normal) curve that is symmetric and centered at 4.1 (with spread consistent with σ = 1.3). Choose the option that shows a normal curve with its peak at 4.1.

(b) We want P(X < 3) for X ~ N(μ = 4.1, σ = 1.3).

Steps:
1. Convert 3 to a standard normal z-score:
z = (3 − 4.1)/1.3 = −1.1/1.3 ≈ −0.846.
2. Use the standard normal CDF: P(X < 3) = Φ(−0.846) ≈ 0.199.

So the probability a CD player breaks down in less than 3 years is about 0.199 (≈ 19.9%, about 20%).