1 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. 4 The probability of a disk drive failure in any week is 0.007. A computer service company maintains 900 disk drives. Use the Poisson distribution to calculate the probability of (a) seven disk drive failures in a week. (b) five (b) more than seven 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 people are away from work? 2 A workforce has on average two people absent through illness on any given day. Find the probability that on a typical day (a) two (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. 3 A machine manufactures 300 micro-chips per hour. The probability an individual chip is faulty is 0.01. Calculate the probability that (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
1 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. 4 The probability of a disk drive failure in any week is 0.007. A computer service company maintains 900 disk drives. Use the Poisson distribution to calculate the probability of (a) seven disk drive failures in a week. (b) five (b) more than seven 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 people are away from work? 2 A workforce has on average two people absent through illness on any given day. Find the probability that on a typical day (a) two (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. 3 A machine manufactures 300 micro-chips per hour. The probability an individual chip is faulty is 0.01. Calculate the probability that (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
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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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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 (b) five 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 (@) two (b) at least three (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 (@) two (b) four (¢) more than three faulty chips are manufactured in a particular hour. Use both the binomial and Poisson approximations and compare the resulting probabilities. [& The probability of a disk drive failure in any week is 0.007. A computer service company maintains 900 disk drives. Use the Poisson distribution to calculate the probability of (a) seven (b) more than seven disk drive failures in a week. 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 people are away from work? 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 (a) none are faulty (b) one is faulty (€) two are faulty (d) three are faulty (e) more than three are faulty I @ o014 @ 00277 2 @ 02707 () 03233 (© 0.8571 @ @ 01435 . (a) Binomial 0.2244; Poisson 0.2240 (b) 0.1689, 0.1680 (¢) 0.353,0.353 (b) 02983
Transcribed Image Text:EXERCISES 29.11
1 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
4 The probability of a disk drive failure in any week is
0.007. A computer service company maintains 900
disk drives. Use the Poisson distribution to calculate
the probability of
(a) nine
(b) five
(a) seven
(b) more than seven
do not function.
disk drive failures in a week.
2 A workforce has on average two people absent
through illness on any given day. Find the probability
that on a typical day
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.
3 A machine manufactures 300 micro-chips per hour.
The probability an individual chip is faulty is 0.01.
Calculate the probability that
(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
2 (a) 0.2707
(c) 0.8571
(b) 0.1689, 0.1680
(c) 0.353, 0.353
(b) 0.3233
(a) 0.1435
(b) 0.2983
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