Page 207 - DMTH404_STATISTICS

Unit 14: Theoretical Probability Distributions

3. A multiple choice test consists of 8 questions with 3 answers to each question (of which Notes
only one is correct). A student answers each question by throwing a balanced die and
checking the first answer if he gets 1 or 2, the second answer if he gets 3 or 4 and the third
answer if he gets 5 or 6. To get a distinction, the student must secure at least 75% correct
answers. If there is no negative marking, what is the probability that the student secures
a distinction?
Hint : He should attempt at least 6 questions.
4. What is the most probable number of times an ace will appear if a die is tossed (i) 50 times,
(ii) 53 times?
Hint : Find mode.
5. The number of arrivals of telephone calls at a switch board follows a Poisson process at an
average rate of 8 calls per 10 minutes. The operator leaves for a 5 minutes tea break. Find
the probability that (a) at the most two calls go unanswered and (b) 3 calls go unanswered,
while the operator is away.
Hint : m = 4.

6. What probability model is appropriate to describe a situation where 100 misprints are
distributed randomly throughout the 100 pages of a book? For this model, what is the
probability that a page observed at random will contain (i) no misprint, (ii) at the most
two misprints, (iii) at least three misprints?
Hint : The average number of misprint per page is unity.
7. If the probability of getting a defective transistor in a consignment is 0.01, find the mean
and standard deviation of the number of defective transistors in a large consignment of
900 transistors. What is the probability that there is at the most one defective transistor in
the consignment?
Hint : The average number of transistors in a consignment is 900 × 0.01.

8. In a certain factory turning out blades, there is a small chance 1/500 for any one blade to
be defective. The blades are supplied in packets of 10. Use Poisson distribution to compute
the approximate number of packets containing no defective, one defective, two defective,
three defective blades respectively in a consignment of 10,000 packets.
Hint : The random variable is the number of defective blades in a packet of 10 blades.

Answers: Self Assessment

1. (b) 2. (a) 3. (d) 4. (b) 5. (c)

14.11 Further Readings

Books Introductory Probability and Statistical Applications by P.L. Meyer
Introduction to Mathematical Statistics by Hogg and Craig
Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor

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