Question

Joan’s finishing time for the Bolder Boulder 10K race was 1.73 standard deviations faster than the women’s average for her age group. There were 410 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan?

Answer 1

Answer:

Approximately 17 women run faster than Joana.

Step-by-step explanation:

We are given the following in the question:

Let $\mu$ and $\sigma$ be the mean and standard deviation of women's finishing time.

We are given that the distribution of finishing is a bell shaped distribution that is a normal distribution.

Then, Joan's finishing time =

$x = \mu + 1.73(\sigma)$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to evaluate

$P(X> x)\\p(x>\mu + 1.73(\sigma))\\\\P(z>\dfrac{x-\mu}{\sigma})\\\\P(z>1.73)$

Calculating value from standard normal table,

$P(z>1.73) =0.0418$

Number of women in Joana's age group, n = 410

Number of women that ran faster than Joana =

$410\times 0.0418 = 17.138\approx 17$

Thus, approximately 17 women run faster than Joana.