Question

(c) z > 1.77 (d) -2.25 < z < 1.77 (a) Find the number z such that the proportion of observations that are less than z in a standard Normal distribution is 0.8. (b) Find the number z such that 35% of all observations from a standard Normal distribution are greater than a NCAA rules for athletes. The National Collegiate Athletic Association (NCAA) requires Division I athletes to score at least 820 on the combined

Answer 1

(a) Given that, P(Z < z) = 0.8, where, Z ~ N(0,1)

Thus, $\Phi$(z) = 0.8 i.e. z = $\Phi^{-1}$(0.8) = 0.842 (Ans).

(b) Given that, P(Z > z) = 0.35 i.e. P(Z $\leq$ z) = 0.65 i.e. $\Phi$(z) = 0.65 i.e. z = $\Phi^{-1}$(0.65) = 0.385 (Ans).

(c) P(Z > 1.77) = 1 - P(Z $\leq$ 1.77) = 1 - $\Phi$(1.77) = 1 - 0.962 = 0.038 (Ans).

(d) P(-2.25 < Z < 1.77) = $\Phi$(1.77) - $\Phi$(-2.25) = 0.962 - 0.012 = 0.95 (Ans).