COMSATS University Islamabad
Department of Computer Science
Terminal Examination – Spring 2021
MTH-262 Statistics & Probability Theory
Program: BSE-IV-A
Date: July 1, 2021.
Time: 16:00-19:00
Instructions for attempting paper:
1. Turn on your camera when asked.
2. Switch off your mobile phones.
3. No extra time will be given for uploading.
4. Cutting and Overwriting is not allowed.
Q. No.1:
Q. No.2:
Q.No.3:
Q.No.4:
Total Marks: 50
Time Allowed: 3 hrs
Instructor: Dr. Masood Anwar
Only write the difference between i) binomial and negative binomial distributions, ii)
binomial and hypergeometric distributions, iii) Poisson and binomial distributions?
In a given city, 5% of all licensed drivers will be involved in at least one car accident in any
given year. Use the Poisson approximation to the binomial distribution to determine the
probability that among 100 licensed drivers randomly chosen in this city (a) only five will be
involved in at least one accident in any given year; (b) at most three will be involved in at least
one accident in any given year.
As part of an air-pollution survey, an inspector decides to examine the exhaust of 6 of a
company’s 24 trucks. If 4 of the company’s trucks emit excessive amounts of pollutants, what
is the probability that at least one of them will be included in the inspector’s sample?
The probability that a student pilot passes the written rest for a private pilot’s license is 0.65.
Find the probability that the student will pass the test (a) on third try (b) before the third try.
Q.No.5:
In an industrial process the diameter of a ball bearings is an important component part. The
buyer sets specifications on the diameter to be 3.0 ± 0.01 cm. The implication is that no part
falling outside these specifications will be accepted. It is known that in the process the
diameter of a ball bearings has a normal distribution with mean 3.0 and standard deviation
0.005. On average how many manufactured ball bearings will be accepted?
Q.No.6:
A pair of dice is rolled 180 times. What is the probability that a same number occurs
(i) at least 25 times (ii) between 32 and 40 times (iii) exactly 29 times.?
Q.No.7:
Suppose that a system contains a certain type of component whose lifetime, in years, to failure
is given by T. The random variable T is modeled nicely by the exponential distribution with
mean time to failure 𝛽 = 5. If 5 of these components are installed in different systems, what
is the probability that at least 1 are still functioning at the end of 5 years?
Q.No.8:
The measurements of the tar content of a certain kind of cigarette yielded 14.4, 13.9, 12.8,
13.5, 15.01,12.8, 13.3, 14,1, 15.5, 14.2, 14.4, 15.3, 12.5, 13.1,14.5, 16.0 and 15.1 mg/cigarette.
Assuming that the data are a random sample from a normal population, use the 0.02 level of
significance to test the hypothesis that the tar content of cigarette exceeds 14.5.
Q.No.9
A fuel oil company claims that one-fourth of the homes in a certain city are heated by oil. Do
we have reason to believe that more than 1/4 are heated by oil if, in a random sample of 1000
homes in this city, it is found 536 are heated by oil? Use a 0.01 level of significance.
Q.No.10: A study was made on the amount of converted sugar in a certain process at various
temperatures. The data was as under;
Temperature:
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Converted sugar:
8.1
7.8
8.5
9.8
9.5
8.9
8.6
10.2 9.3
9.2
a) Estimate the linear regression line.
b) Estimate the mean amount of converted sugar produced when the coded temperature is 1.75.
c) Compute and interpret correlation coefficient.
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