Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of , Google's Chrome browser exceeded a market share for the first time, with a share of the browser market (Forbes website, December ). For a randomly selected group of Internet browser users, answer the following questions. a) Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.
b) Compute the probability that at least 3 of the 20 Internet browser users use Internet browser.
c) For the sample of 20 Internet browser users, compute the expected number of Chrome users.
d) For the sample of 20 Internet browser users, compute the variance and standard deviation for the numbers of Chrome users.

Step-by-step explanation:

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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 (Forbes website, December 15, 2014). For a randomly selected group of 20 Internet browser users, answer the following questions.

a.Compute the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser.

b.Compute the probability that at least 3 of the 20 Internet browsers users use Chrome as their Internet browser.

c.For the sample of 20 Internet browser users, compute the expected number of Chrome users.

d.For the sample of 20 Internet browser users, compute the variance and standard deviation for the number of Chrome users.

Solution:

Let x be a random variable representing the number of internet browsers users that use chrome. This is a binomial distribution since the outcomes are two ways. It is either they used chrome browser or they don't use it. The probability of success, p = 20.37/100 = 0.2037

The probability of failure, q = 1 - p

q = 1 - 0.2037 = 0.7963

a) The the probability that exactly 8 of the 20 Internet browser users use Chrome as their Internet browser, P(x = 8) is determined from the binomial probability calculator.

x = 8

n = 20

p = 0.2037

P(x = 8) = 0.024

b) P(x ≥ 3) = 0.81

c) the expected number of Chrome users is the mean.

mean = np

mean = 20 × 0.2037 = 4.074

d) Variance = npq = 20 × 0.2037 × 0.7963

Variance = 3.244

Standard deviation = √npq

Standard deviation = √3.244 = 1.8

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