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.



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

I can do Part B right away; for Part A I need to see the graphs (or their descriptions) to pick the correct one.

Part B — probability a player breaks down in less than 3 years

1. Let X ~ Normal(μ = 4.1, σ = 1.3). We want P(X < 3).
2. Convert to a standard normal z:
z = (3 − 4.1) / 1.3 = −1.1 / 1.3 ≈ −0.846.
3. Look up Φ(−0.846) (the standard normal CDF). Using a z‑table or calculator,
Φ(−0.846) ≈ 0.1988.

So the probability is about 0.199 (about 19.9%).

Part A — which graph
- I can’t see the four graphs you mention. To choose the correct one, pick the graph that shows a symmetric bell curve centered at 4.1 (the mean) with inflection points at about 4.1 ± 1.3 (≈ 2.8 and 5.4). If you can upload or describe the four options, I’ll pick the correct letter.