The following table contains the probability distribution for X = the number of traffic

accidents reported in a day in a small city in the Midwest:

a) What is the probability of at least 1 accident?

b) What is the expected number of accidents?

c) What is the variance of the number of accidents?

d) What is the standard deviation of the number of accidents?

**Pblem 4**. (10 points) A company that sells annuities must base the annual payout on the probability distribution of the length of the life of the participants in the plan. Suppose that the probability distriution of the lifetimes of the participants is Normally distributed with a mean of 68 years and a standard deviation of 3.5 years.

a) What is the probability that a plan recipient receives payments beyond age 75?

b) What is the probability that a plan recipientd ies before they reach the standard retirement age of 65?

c) Find the age at which payments have ceased for 86% of the plan participants.