Question

a certain flight arrives on time percent of the time. suppose flights are randomly selected. use the normal approximation to the binomial to approximate the probability that ​(a) exactly flights are on time. ​(b) at least flights are on time. ​(c) fewer than flights are on time. ​(d) between and ​, inclusive are on time.

Answer 1

The probability that exactly 128 flights are on time is 88.27% and the probability that atleast 1 flight is on time is 0.022.

Given that the chances of reaching the flight on time be 88%.

We are required to find the probability that exactly 128 flights are on time, atlleast 1 flight on time.

Probability is basically the calculation of likeliness of happening an event among all the events possible. It lies between 0 and 1.

Probability=Number of items/Total items.

It cannot be negative.

Probability that the flight will be on time if one flight is selected=0.88

Probability that exactly 128 flights are on time=

128=1145*P/100

P=12800/145

P=88.27%

b) Atleast 1 flight is on time

=($128C_{0}(0.88)^{0} (0.12)^{1}$+$128C_{1} (0.88)^{1} (0.12)^{11}$)/128

=(0.12+128*0.88*0.245)/128

=(0.12+2.575)/128

=0.022

Hence the probability that exactly 128 flights are on time is 88.27% and the probability that atleast 1 flight is on time is 0.022.

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