Question

When Aria goes bowling, her scores are normally distributed with a mean of 165 anda standard deviation of 13. Out of the 150 games that she bowled last year, how manyof them would she be expected to score less than 149, to the nearest whole number?

Answer 1

Given:

mean, μ = 165

Standard deviation, σ = 13

n = 150

Let's find how many of them she would expect to score less than 149.

Apply the z-score formula:

`z=(x-\mu)/(\sigma)`

Thus, we have the z-score:

`\begin{gathered} z=(149-165)/(13) \\ \\ z=(-16)/(13) \\ \\ z=−1.23 \end{gathered}`

Here, we are to solve for: P(x < 149).

We have:

P(x < 149) = P(z < -1.23)

Using the standard normal table, we have:

NORMSDIST(-1.23) = 0.10935

Therefore, out of the 150 games, the expected score less than 149 would be:

150 x 0.10934 = 16.4 ≈ 16

The expected number to score le