A search engine company claims that 15% of people who use its site click for mor

Question

A search engine company claims that 15% of people who use its site click for more information about its advertisers’ products. Assuming that claim is true,

(a) what is the probability that at least one out of the next 8 people who use the site will click for more information?

(b) Estimate, using the normal distribution, the probability that at least 10 out of the next 80 people who use the site will click for more information.

(c) Write a few sentences describing why the answer to (b) is higher than the answer to part (a). Why would the answer be even higher if you estimated the probability that at least 1000 out of 8000 click for more info?

Explanation / Answer

Here it is given that,

p = 0.15

a)

n = 8

P ( x >= 1 ) = 1 – P ( x = 0 )

This is Binomial Distribution:

P (x = 0) = C (8,0) *0.15^0 * (1-0.15)^(8-0)

             = 1 * 1 * 0.2725

             =0.7275

Answer: 0.7275

b)

n = 80

Mean = np = 80 *0.15 = 12

Standard deviation (SD) = Önpq

                                            = Ö(80*0.15*0.85)

                                           = 3.1937

P ( x 10 ) = P ( x 9.5 ) ; 0.5 is the correction factor.

Z = ( x – Mean ) / Standard deviation

= (9.5 – 12 )/3.1937

= -0.78

P (z -0.78) = 1 – P ( z < -0.78 )

                      = 1 – 0.2177

                      = 0.7823

Answer: 0.7823

( c )

In part ( b ) the sample size gets increased ( the value of x also gets increased ) so the obtained probability is higher compare to part ( a ). If we are going to find the probability of at least 1000 among 8000 here also the probability will be high as the sample size get increased and the value of x also gets increased.

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