According to the American Payroll Association

(September 10, 2004), when asked, “Do you support the use of biometric technology (fingerprints or hand recognition) to record employee time and attendance?” the majority of workers say they wouldn’t mind. However, 28% object to it, believing it is an invasion of personal privacy. To better understand the extent of this objection, consider the variable x to be the number of people in a sample of 25 who say they “object.” Assume the 28% is true for the whole population of workers and that a random sample is selected.

a. Is x a binomial random variable? Justify your answer.

b. Find the probability that x has a value from 4 to 10.

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 to x  10, 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.