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 [tex]\sim[/tex] Normal (250 , 15)
Let Z = [tex]\frac {(X - 250)}{15}[/tex] -----------------------(1)
So, Z [tex]\sim[/tex] Normal (0, 1)
According to the question, the bottom 95% in the tryout scorecard are to be eliminated.
Let, P(Z ≤ [tex]z_{0.95}[/tex]) = 0.95
Now, from the inverse standard normal probability table,
[tex]z_{0.95}[/tex] = 1.645
So, if we say that
P(X ≤ [tex]x_{0.95}[/tex]) = 0.95, then
[tex]x_{0.95} = z_{0.95} \times 15 + 250[/tex] --------------[from (1)]
= [tex]1.645 \times 15 + 250[/tex]
= 274. 675
Hence, from the given options, the answer is, 274.
