According to United Mileage Plus Visa (November 22, 2004), 41% of passengers say they “put on the earphones” to avoid being bothered by their seatmates during flights. To show how important, or not important, the earphones are to people, consider the variable x to be the number of people in a sample of 12 who say they “put on the earphones” to avoid their seatmates. Assume the 41% is true for the whole population of airline travelers and that a random sample is selected.
a. Is x a binomial random variable? Justify your answer.
b. Find the probability that x _ 4 or 5.
c. Find the mean and standard deviation of x.
d. Draw a histogram of the distribution of x: label it completely, highlight the area representing x _ 4 and x _ 5 draw a vertical line at the value of the mean, and mark the location of x that is 1 standard deviation larger than the mean.