Question

In university’s football team average weight of players is around (60 + α) kg, and the standard deviation is 4.37 lbs. Assuming heights are normally distributed (a) What percentage of players are heavier than 70 kg? (b) If your favorite player is within the heaviest (α+12)% of all players, what can his weight be?

Answer 1

a)

$P(X>70)=P(Z>\frac{70-(60+\alpha)}{4.37})=\\ 1-P(Z\le\frac{10-\alpha}{4.37})=1-Z_{\frac{10-\alpha}{4.37}}$

b)

$x=60+\alpha + 4.37*Z_{1-\frac{12+\alpha}{100}}$

Hence, his weight is more than $60+\alpha + 4.37*Z_{1-\frac{12+\alpha}{100}}$