10km race

Joan's finishing time for the Bolder Boulder 10 km race was 1.77 standard deviations faster than the women in her age group. 415 women ran in her age group. Assuming a normal distribution, how many women ran more quickly than Joan?

Correct answer:

x =  15

Step-by-step explanation:

$$\begin{gathered} z=1.77\sigma \\ w=415 \\ n=0.4616 \\ r=0.50-0.4616=0.0384 \\ {x}_1=r\cdot w=0.0384\cdot 415=\frac{1992}{125}=15\frac{117}{125}=15.936 \\ x=\lfloor x_1\rfloor =\lfloor 15.936\rfloor =15 \end{gathered}$$

Use the normal distribution table.

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