Question

A club volleyball league allows only the top 5% of athletes who try out to be part of the team. If the team tryout scorecard has a mean of 250 and a standard deviation of 15, which of the following can be used as a minimum qualifying score to join the volleyball league? 13 237 251 274

Answer 1

Answer:

Among the given options, the one which can be used as a minimum qualifying score to join the volleyball league is, 274.

Step-by-step explanation:

Let the team tryout scorecard is represented by the random variable X.

Now, according to the question,

X $\sim$ Normal (250 , 15)

Let Z = $\frac {(X - 250)}{15}$  -----------------------(1)

So, Z $\sim$ Normal (0, 1)

According to the question, the bottom 95% in  the tryout scorecard are to be eliminated.

Let,  P(Z ≤ $z_{0.95}$) = 0.95

Now, from the inverse standard normal probability table,

$z_{0.95}$ = 1.645

So, if we say that

P(X ≤ $x_{0.95}$) = 0.95, then

$x_{0.95} = z_{0.95} \times 15 + 250$ --------------[from (1)]

                    = $1.645 \times 15 + 250$

                    = 274. 675

Hence, from the given options, the answer is, 274.

Answer 2

Answer:

274

Step-by-step explanation: