A Fidelity life insurance company charges $226 for a $50,000 life insurance policy for a 50-year-old female. The probability that such a female survives the year is 0.9968 (based on data from the U.S. Department of Health and Human Services). Assume that the company sells 700 such policies to 50-year-old females, so it collects $158,200 in policy payments. The company will make a profit if fewer than four of the 700 women die during the year.

a. What is the mean number of deaths in such groups of 700 females?

b. Find the probability that the company makes a profit from the 700 policies. Is that probability high enough so that the company is almost sure to make a profit?