The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is one of the busiest in the world with an average of 60 births per day. Let X = the number of births in an hour. a. Find the mean and standard deviation of X. b. Sketch a graph of the probability distribution of X. c. What is the probability that the maternity ward will deliver three babies in one hour? d. What is the probability that the maternity ward will deliver at most three babies in one hour? e. What is the probability that the maternity ward will deliver more than five babies in one hour?

The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of $X . X \sim$ (____,) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average. f. Find the probability that she has more children than the Japanese average.

The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year. a. Find the mean waiting time between accidents. b. Find the standard deviation of the waiting times between accidents. c. Find the probability that more than one year elapses between accidents. d. Find the probability that less than one month elapses between accidents. e. If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?

In a maternity ward, four babies become accidentally mixed up. The ABO types of the four babies are known to be O, A, B, and AB. The ABO types of the four sets of parents are determined. Indicate which baby belongs to each set of parents:

$$\text { (a) } A B \times O , ( b ) A \times O , ( c ) A \times A B \text { (d) } \mathrm { O } \times \mathrm { O }$$

An ectopic pregnancy is twice as likely to develop when the pregnant woman is a smoker as it is when she is a nonsmoker. If 32 percent of women of childbearing age are smokers, what percentage of women having ectopic pregnancies are smokers?

Rabies virus and poliovirus both have single-stranded RNA genomes, but only in poliovirus can the genome be translated directly. Explain.