Question

32.71% of Delta Airlines were never on time in 2016. Assume this percentage still holds true for airline. For the next 31 flights from Delta Airlines, use the normal approximation to the binominal distribution to answer the following questions.

a) Find the probability that exactly 9 flights will arrive on time.

b) Find the probability that fewer than 15 flights will arrive on time.

c) Find the probability that 21, 22, or 23 flights will arrive on time.

Answer 1

This is a binomial distribution question with

n = 31

p = 0.71

q = 1 - p = 0.29

This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5

Since we know that

a)

P(X = 9.0) = ?

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

P(X = 9.0) = 0

b)

P(x < 15.0)=?

The z-score at x = 15.0 is,

z = -2.7747

This implies that

c)

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