Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
Central Limit Theorem
1. The probability that an inquiry leads to a sale is 0.7, independently for each inquiry. Over a period of
time, 200 such inquiries are received. By making suitable approximations, estimate the probability
that the number of sales from inquiries is more than 145.
2. The number of automobile accidents each year in a particular suburb of Chicago is modeled using a
Poisson distribution with mean 225. Using the Central Limit Theorem, calculate the approximate
probability that the number of motor accidents in a given year is more than 230 but at most 247.
3. An insurance company has 180 policy holders. An actuary has determined that the probability that a
policy holder makes a claim in a given year is 1/6. Find the approximate probability that the number
of claims is no more than 40 in a year.
4. The number of claims arriving at an insurance office per day can be modeled by a Poisson
distribution with mean 10. In a working week of 5 days, calculate the approximate probability that
the number of claims received lies strictly between 46 and 52.
5. An insurer has studied the claim amounts that arise from policies and has discovered that claim
amounts follow a lognormal distribution with parameters m = 5 and s2 = 4. The insurer predicts that
next year's claim amounts are going to increase 4% from this year's values. Calculate the probability
that next year a claim exceeds 2,000.
6. Salaries in a large insurance company are distributed with mean 43,500 and standard deviation
10,000. Calculate the probability that the mean salary of a selected sample of 120 workers from this
company is greater than 45,000.