Question

A certain flight arrives on time 90 percent of the time. Suppose 190 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 163 flights are on time.

​(b) at least 163 flights are on time.

​(c) fewer than 182 flights are on time.

​(d) between 182 and 183​, inclusive are on time.

Answer 1

This is a binomial distribution question with
n = 190
p = 0.9
q = 1 - p = 0.1
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that


a)


b)

The z-score at x = 162.5 is,

z = -2.0555
This implies that


c) P(x < 182.0)=?
The z-score at x = 182.0 is,

z = 2.6601
This implies that


d)

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