A search engine company claims that 12% of people who use its site click for mor

Question

A search engine company claims that 12% 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 10 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 100 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 10000 click for more info?

Explanation / Answer

a) p = 0.12

Binomial dist

P(X 1) = 1 - P(0)

P = 1 - 10C0 * 0.12^0 * 0.88^10

P = 0.72

b) Mean = n * p

Mean = 100 * 0.12 = 12

SD = sqrt(12 * 0.88)

SD = 3.25

X = 10

z = (10 - 12)/3.25

z = - 0.62

P = 0.7324

c) We should see that we would benefit from making some kind of correction for the fact that we are using a continuous distribution to approximate a discrete distribution.

Normal approx probablity will rise above binomial as 'n' keeps on increasing

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