Question

According to a recent report, 68% of Internet searches in a particular month used the Google search engine. Assume that a sample of 22 searches is studied. Round the answers to four decimal places.

(a) What is the probability that exactly

19

of them used Google?

The probability that exactly 19 of them used Google is .

Part 2 of 4

(b) What is the probability that

14

or fewer used Google?

The probability that 14 or fewer used Google is .

Part 3 of 4

(c) What is the probability that more than

19

of them used Google?

The probability that more than 19 of them used Google is .

Part 4 of 4

(d) Would it be unusual if fewer than

12

used Google?

It ▼(Choose one) be unusual if fewer than 12 used Google since the probability is .

Answer 1

According to a recent report, 68% of Internet searches in a particular month used the Google search engine. Assume that a sample of 22 searches is studied. Round the answers to four decimal places.

This is a binomial event since there are two outcomes either searched using google search engine or not. For each user the probability of using google is same. There are more than 1 independent trials.

(n = 22 ,p = 68% = 0.68 )

P(X=x) =

P(X= x) =

X	P (X = x)
0	0.0000
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0001
7	0.0004
8	0.0017
9	0.0057
10	0.0158
11	0.0365
12	0.0712
13	0.1163
14	0.1589
15	0.1801
16	0.1674
17	0.1256
18	0.0741
19	0.0332
20	0.0106
21	0.0021
22	0.0002
Total	1.0000

(a) What is the probability that exactly

19

of them used Google?

P(X = 19) =

The probability that exactly 19 of them used Google is 0.3316 .

Part 2 of 4

(b) What is the probability that

14

or fewer used Google?

That means at the most 14

P( X 14 ) = 1 - P(X > 14)

= 1 - [P(X = 15) + P(X =16 ) + P(X =17 ) + P(X = 18) + P(X = 19)+ P(X =20 ) +P(X =21 )+ P(X =22 )] ...............this is a the complementary rule where P(A') = 1- P(A)

= 1 - 0.5933

The probability that 14 or fewer used Google is 0.4067

Part 3 of 4

(c) What is the probability that more than

19

of them used Google?

P(X > 19) = P(X =20 ) +P(X =21 )+ P(X =22 )

The probability that more than 19 of them used Google is  0.129.

Part 4 of 4

(d) Would it be unusual if fewer than

12

used Google?

To be unusual the probability needs to be less than 0.05.

P(X < 12) = P(X = 0) + P( X = 1) + ......P(X = 11)

= 0.0603

> 0.05

So it not unusual.

It will not be unusual if fewer than 12 used Google since the probability is 0.0603..