Question

Google it: According to a recent report, 66% of Internet searches in a particular month used the Google search engine. Assume that a sample of 23 searches is studied. Round the answers to at least four decimal places. Part 1 of 4 (a) What is the probability that exactly 20 of them used Google The probability that exactly 20 of them used Google is : Part 2 of 4 (b) What is the probability that 15 or fewer used Google? The probability that 15 or fewer used Google is Part 3 of 4 (c) What is the probability that more than 20 of them used Google? The probability that more than 20 of them used Google is .

Answer 1

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This is a typical example of Binomial distribution...

Here n = 23 (sample size)

p =0.66 (probability of success)

i.e, P(X=x) = ²³C_x * 0.66^x * 0.34^23-x for all x = 0,1,2,...,23

a)

P(X=20) = ²³C₂₀ * 0.66²⁰* 0.34^23-20 = 0.01712119301

b)

P(X < or = 15) = Sum of all x from 0 to 15 { ²³C_x * 0.66^x * 0.34^23-x } = 0.54645864283

c)

P(X > 20) = Sum of all x from 21 to 23 { ²³C_x * 0.66^x * 0.34^23-x } =  0.00565647231

d)

It would be unusual

Probability = 0.12033818793