Question

A competitive cheer team allows only the top 4% of athletes who try out to be part of the team. If the team tryout scorecard has a mean of 200 and a standard deviation of 10, which of the following can be used as a minimum qualifying score to join the cheer team?
A.) 8
B.) 192
C.) 217
D.) 202

Answer 1

Answer:

C.) 217

Step-by-step explanation:

If the top 4% of athletes are allowed to be part of the team, then the bottom $1-4\%=96\%$  will not qualify.

We look for a z-score below which $96\%$ of the population lie.

Reading from the z-table as shown in the attachment, this z-value corresponds to $1.74$.

We now use the z-score formula to find the required minimum qualifying score.

$Z=\frac{x-\mu}{\sigma}$

where $\mu=200,\sigma=10,and\:z=1.74$

We substitute and solve for x.

$1.74=\frac{x-200}{10}$

$x-200=17.4$

$x=200+17.4$

$x=217.4$

$x\approx217$

The correct choice is C