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.

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

Answer 1

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

1. Convert to a standard normal z-score:
z = (3 − 4.1)/1.3 = −1.1/1.3 ≈ −0.846.

2. Use the standard normal table or a calculator to find Φ(−0.846):
Φ(−0.846) ≈ 0.199.

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