A recent survey found that 72 % of adults over 50 wear glasses for driving. You randomly select 33 adults over 50, and ask if he or she wears glasses.

Use the normal approximation to approximate binomial distribution.

1. A recent survey found that 72 % of adults over 50 wear glasses for driving. You randomly select 33 adults over 50, and ask if he or she wears glasses. Decide whether you can use the normal approximation to approximate binomial distribution. If so, find the mean and standard deviation. If not, explain why?

2. The failure rate in a statistics class is 10 %. In a class of 40 students, find the probability that exactly 5 students will fail. (use the normal approximation to approximate binomial distribution.)

3. A student answers 48 questions on a multiple-choice test by guessing. Each question has four possible answers only one of which is correct. Find the probability that the student gets exactly 15 correct answers. (use the normal approximation to approximate binomial distribution.)

4. If the probability of a newborn child being female is 0.5. Find the probability that in 100 births, 55 or more will be female.

5. 65 % of U.S. college graduates are employed in their field of study. You randomly select 20 U.S. college graduates and ask them whether they are employed in their field of study. Find the probability that the number who are employed in their field of study is less than 10. (use the normal approximation to approximate binomial distribution.)