30% of the population has type A blood. 

(a)     If 8 people are selected at random, what is the probability that at least four of them have type A blood.

(b)     If 80 donors come to give blood one day, what is the probability that at least forty of them have Type A blood (using the normal approximation)?  Explain why this is higher or lower than the answer in part (a).

(c)      If 20 people come to give blood, what is the probability that at least one of the donors is of Type A?

2.      The Federal Reserve reports that the mean lifespan of a five dollar bill is 4.9 years.   Let’s suppose that the standard deviation is 1.8 years and that the distribution of lifespans is normal. Find:

(a)      the 98^th  percentile for the lifespan of these bills (a time such that 98% of bills last less than that time).

(b)      the probability that a random sample of 35 bills has a mean length of more than 4 years.

3.      A health insurance company charges policyholders a $1250 annual premium for health insurance for hospitalization.  The company estimates that each time a patient is hospitalized costs the company $2500.  Furthermore, they have estimated that 80% of patients will not be hospitalized, 15% will be hospitalized once a year, and no one will be hospitalized more than twice. 

(a)     Find the insurance company’s expected profit per policyholder. 

(b)     What is the expected profit if they enroll 80,000 policyholders?

4.  The IRS computes the time it takes filers to complete its forms.  For a particular form, the completion times are normally distributed with a mean of 55.5 minutes and a standard deviation of 11.2 minutes.

(A)  What is the probability that it takes an individual filer more than 60 minutes to complete the form?

(B)  Find a time such that 85% of all forms can be completed in less than that time.

(C)  An accounting firm has 21 of these forms to complete one day.  What is the probability that the mean completion time for the 10 forms is over 60 minutes?