A computer network has several hundred computers. During an 8 hour period, there are on average seven computers not functioning. Find the probability that during an 8 hour period (a) nine do not function. 1 (b) five
A computer network has several hundred computers. During an 8 hour period, there are on average seven computers not functioning. Find the probability that during an 8 hour period (a) nine do not function. 1 (b) five
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:EXERCISES 29.11
4 The probability of a disk drive failure in any week is
0.007. A computer service company maintains 900
A computer network has several hundred computers.
During an 8 hour period, there are on average seven
computers not functioning. Find the probability that
during an 8 hour period
(a) nine
1
disk drives. Use the Poisson distribution to calculate
the probability of
(b) five
(a) seven
disk drive failures in a week.
(b) more than seven
do not function.
A workforce has on average two people absent
through illness on any given day. Find the probability
that on a typical day
5 The probability an employee fails to come to work is
0.017. A large engineering firm employs 650 people.
What is the probability that on a particular day
(a) nine
(b) 10
(a) two
people are away from work?
(b) at least three
6 A machine manufactures electrical components for
the car industry at the rate of 750 per hour. The
probability a component is faulty is 0.013. Use both
the binomial distribution and the corresponding
Poisson approximation to find the probability that in a
sample of 200 components
(c) less than four
people are absent.
A machine manufactures 300 micro-chips per hour.
The probability an individual chip is faulty is 0.01.
Calculate the probability that
3
(a) two
(a) none are faulty
(b) four
(b) one is faulty
(c) more than three
(c) two are faulty
faulty chips are manufactured in a particular hour. Use
both the binomial and Poisson approximations and
compare the resulting probabilities.
(d) three are faulty
(e) more than three are faulty
Solutions
1
(a) 0.1014
(b) 0.1277
3 (a) Binomial 0.2244; Poisson 0.2240
(b) 0.1689, 0.1680
(a) 0.2707
(b) 0.3233
(c) 0.353, 0.353
(c) 0.8571
4 (a) 0.1435
(b) 0.2983
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