Problem
According to surveys done by the National Retail Federation (NRF) last year, 49.5% of holiday shoppers bought something online during the Cyber Monday sales event. We know the sample proportion () would vary for repeated sampling. Let's say that the sampling distribution for () is approximately normal with a mean of 0.495 and standard deviation of 0.011.
a) Find the probability that at least 0.500 of shoppers bought something online during the Cyber Monday sales. Draw the density curve, be sure to label and shade.
b) Find the probability that between 0.485 and 0.515 of shoppers bought something online during the Cyber Monday sales. Draw the density curve, be sure to label and shade.