Question

A certain flight arrives on time 82 percent of the time. Suppose 193 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 159 flights are on time.

​(b) at least 159 flights are on time.

​(c) fewer than 152 flights are on time.

​(d) between 152 and 173​, inclusive are on time.

Answer 1

This is a binomial distribution question with

n = 193

p = 0.82

q = 1 - p = 0.18

This binomial distribution can be approximated as Normal distribution since

np > 5 and nq > 5

Since we know that

a) P(X = 159.0) = ?

For a continuous the probability is the integration of probability density function in a given interval. Since if we give a particular point as an interval the integration comes out as 0.

P(X = 159.0) = 0

b)

The z-score at x = 158.5 is,

z = 0.045

This implies that

c) P(x < 152.0)=?

The z-score at x = 152.0 is,

z = -1.1729

This implies that

d) P(152.0 < x < 173.0)=?

This implies that

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