Question

Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google's Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market.† For a randomly selected group of 25 Internet browser users, answer the following questions. (Round your answers to four decimal places.)

(a)

Compute the probability that exactly 7 of the 25 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(b)

Compute the probability that at least 3 of the 25 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(c)

For the sample of 25 Internet browser users, compute the expected number of Chrome users.

(d)

For the sample of 25 Internet browser users, compute the variance and standard deviation for the number of Chrome users. (Round your answers to four decimal places.)

variancestandard deviation

Answer 1

p = 0.2037

n = 25

This is a binomial distribution.

P(X = x) = 25Cx * 0.2037^x * (1 - 0.2037)^25-x

a) P(X = 7) = 25C7 * 0.2037⁷ * 0.7963¹⁸ = 0.1159

b) P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

                   = 1 - (25C0 * 0.2037⁰ * 0.7963²⁵ + 25C1 * 0.2037¹ * 0.7963²⁴ + 25C2 * 0.2037² * 0.7963²³)

                   = 1 - 0.0909

                   = 0.9091

c) expected value = n * p = 25 * 0.2037 = 5.0925 or 5 (approx)

d) variance = n * p * (1 - p) = 25 * 0.2037 * (1 - 0.2037) = 4.0552

standard deviation = sqrt(n * p * (1 - p)) = sqrt(25 * 0.2037 * (1 - 0.2037)) = 2.0137