A certain flight arrives on time 8989 percent of the time. Suppose 153153 flight

ID: 3291057 • Letter: A

Question

A certain flight arrives on time

8989

percent of the time. Suppose

153153

flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly

133133

flights are on time.(b) at least

133133

flights are on time.(c) fewer than

124124

flights are on time.(d) between

124124

and

132132,

inclusive are on time.

(a)

P(133133)equals=0.0740 0.0740

(Round to four decimal places as needed.)(b)

P(Xgreater than or equals133133)equals=nothing

(Round to four decimal places as needed.)

Ans:

Binomial distribution:

n=153

p=0.89

Normal approximation to the Binomial:

Mean=np=153*0.89=136.17

Standard dev=sqrt(np(1-p))=sqrt(136.17*0.11)=3.870

a)P(x=133)=NORMDIST(133,136.17,3.87,FALSE)=0.0737

b)P(x>=133)=1-P(x<=132)=1-NORMDIST(132,136.17,3.87,TRUE)=1-0.1406=0.8594

c)P(x<124)=NORMDIST(123,136.17,3.87,TRUE)=0.0003

d)P(124<=x<=132)=P(x<=132)-P(x<=124)=0.1406-0.0008=0.1398

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