MCB1007 Introduction to Probability and Statistics Fall 2017-2018
Final Exam
December 18, 2017
No:
Name:
Section:
Justify your answers to get full credit − Exam Duration 90 Minutes 1) An expensive item is being insured against early failure. The lifetime of the item is
normally distributed with a mean of 7 years and a standard deviation of 2 years. The insurance will pay a dollars if the item fails during the first or second year and a/2 dollars if the item fails during the third or fourth year. If a failure occurs after the fourth year, then the insurance pays nothing. How to choose a such that the expected value of the payment per insurance is $50?
Answer.
1 / 15
2 / 10
3a / 9
3b / 8
3c / 8
4 / 12
5a / 6
5b / 10
6 / 10
7 / 12
P /100
2) The probability that a drug cures a patient is 90%. Use a normal distribution to approximate the probability that at least 56 out of 60 people who take the drug are cured.
Answer.
3) A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of 120 homeowners selected from this area showed that they pay an average of 1575$ per month. The population standard deviation of such mortgages is 215$.
a) Find a %97 confidence interval for the mean amount of mortgage paid per month by all homeowners in this area.
Answer.
b) With what degree of confidence could we say that the mean amount of mortgage paid per month is 1575 ± 34.
Answer.
c) What should be the minimum sample size, if error does not exceed 35?
Answer.
4) Number of customers who visited a company that is set up 13 days ago are recorded in the following table. Estimate mean number, median and the modal class of customers.
Number of Days Number of Customers
2 − 4 14
5 − 7 13
8 − 10 3
11 − 13 20
Answer.
5) From the set of numbers {1, 5, 9} a random sample of size 2 will be selected without replacement.
a) Find the mean and the standard deviation of the population Answer.
b) Find the mean and the standard deviation of the sampling distribution Answer.
6) There are 300 employees in a company, 240 of whom are trade union member. 6 employees will be selected randomly among all employees for the commission, what is the probability that 4 of which are trade union member?
Answer.
7) A dry cleaner receives 3 complaints on average in a day. What is the probability that this dry cleaner receives 10 complaints in a week.
Answer.
