An investment website can tell what devices are used to acce

An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smart phones, so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of 300 investors from their customers. Suppose that the true proportion of smart phone users is 41%. What is the probability that the sample proportion is greater than 0.48?

Solution

So the probability that the sample proportion is greater than 0.48 is

P(phat>0.48) = P((phat-p)/sqrt(p*(1-p)/n) >(0.48-0.41)/sqrt(0.41*(1-0.41)/300))

=P(Z>2.47) =0.0068 (from standard normal table)