Math 419 – Spring 2016
REVIEW:
1
Limits, Central Limit Theorem
Problem Set 7
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
Limits, 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
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
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
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
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
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
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
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
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
Math 419 – Spring 2016
Limits, Central Limit Theorem
Problem Set 7
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.
7