Question

A certain flight arrives on time 86 percent of the time. Suppose 162 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 152 flights are on time. (b) at least 152 flights are on time. c) fewer than 144 flights are on time. (d) between 144 and 147, inclusive are on time. a) P(152)= (Round to four decimal places as needed.)

Answer 1

a certain flight arrive on time: p = 0.86

total number of flight: n=162

J K L 0.86 162 formula used a) Probability that exactly 152 flights are on time = P(X=152)= 0.000826733 BINOMDIST(152,C3, C2,FALSE) b) Probability that at least 152 flights are on time P(X2152)= PIX<152) 1-P(X<152) = 0.998670981 0.001329 BINOMDIST(151,C3,C2, TRUE) c) Probability that fewer than 144 flights are on time = P(X<144) = 0.827510618 BINOMDIST(143,C3,C2, TRUE) d) probability that between 144 and 147, inclusive are on time = P(1445XS147)= P(XS147) - PIXS143) P(1445XS147)= 0.145938 F14-F15 PIXS147)= P(XS143)= 0.973448547 0.827510618