Question

According to a recent report,

67%

of Internet searches in a particular month used the Google search engine. Assume that a sample of

24

searches is studied. Round the answers to four decimal places.

Part 1 of 4

(a) What is the probability that exactly

21

of them used Google?

Part 2 of 4

(b) What is the probability that

16

or fewer used Google?

Part 3 of 4

(c) What is the probability that more than

21

of them used Google?

Part 4 of 4

(d) Would it be unusual if fewer than

14

used Google?

Answer 1

here this is binomial with parameter n=24 and p=0.67

a)

P(X=21)=

(nCx)px(1−p)(n-x)    =

0.0162

b)

P(X<=16)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.5625

c)

P(X>=22)=1-P(X<=21)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.0053

d)

P(X<14)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.1322

since probabilty of less than 14 is not less than 0.05 , this is not an unusual event