Distributionshard
0:00.0

Let X1,X2,,X100X_1, X_2, \dots, X_{100} be i.i.d. standard normal random variables. Let Yi=I(Xi>0.84)Y_i = I(X_i > 0.84), where II is the indicator function, and note that the standard normal CDF satisfies Φ(0.84)0.80\Phi(0.84) \approx 0.80. Let S=i=1100YiS = \sum_{i=1}^{100} Y_i. Using the normal approximation with a continuity correction, find the approximate value of P(S15)P(S \le 15) expressed in terms of the standard normal CDF Φ\Phi.