Question

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.

Math

Answer 1

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

1. Standardize: z = (3 − 4.1)/1.3 = −1.1/1.3 ≈ −0.846.
2. Look up the standard normal CDF: P(X < 3) = Φ(−0.846). Using a normal table or calculator, Φ(−0.846) ≈ 0.199.

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