In an online survey of 4001 respondents, 8% were classified as productivity enhancers who are comfortable with technology and use the internet for its practical value. Suppose you select a sample of 400 students at your school, and the population proportion of productivity enhances is .08.
a. What is the probability that in the sample, fewer than 10% of the students will be productivity enhancers?
b. What is the probability that in the sample, between 6% and 10% of the students will be productivity enhancers?
c. What is the probability that in the sample, more than 5% of the students will be productivity enhancers?
d. If a sample of 100 is taken, how does this change your answers to (a) through (c)?