Q4/ The number of messages sent to a computer bulletin board is a Poissor random variable with a mean of 5 messages per hour. (a) What is the probability that 5 messages are received in 1 hour? (b) What is the probability that 10 messages are received in 1.5 hour? | Engineering Statistics (c) What is the probability that less than two messages are received in one-hal hour?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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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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(d) mean and variance of X
Ans. (0.3681, 0.6319,0.9198, 1,0.999)
Q4/ The number of messages sent to a computer bulletin board is a Poisson
random variable with a mean of 5 messages per hour.
(a) What is the probability that 5 messages are received in 1 hour?
(b) What is the probability that 10 messages are received in 1.5 hour?
Engineering Statistics
(c) What is the probability that less than two messages are received in one-half
hour?
Ans. (0.1755, 0.0858, 0.2873)
Q5/ The number of flaws in bolts of cloth in textile manufacturing is assumed to be
Poisson distributed with a mean of 0.1 flaw per square meter.
(a) What is the probability that there are two flaws in 1 square meter of
(b) What is the probability that there is one flaw in 10 square meters of cloth?
(c) What is the probability that there are no flaws in 20 square meters of cloth?
(d) What is the probability that there are at least two flaws in 10 square meters
th?
of cloth?
Ans. (0.0045, 0.3679, 0.1353,0.2642)
Q6/ The number of failures for a cryogenics machine from contamination in
biological samples is a Poisson random variable with a mean of 0.01 per 100
samples.
(a) If the lab usually processes 500 samples per day, what is the expected
number of failures per day?
(b) What is the probability that the machine will not fail during a study that
includes 500 participants? (assume one sample per participant.)
Ans. (0.05, 0.9512)
Transcribed Image Text:(d) mean and variance of X Ans. (0.3681, 0.6319,0.9198, 1,0.999) Q4/ The number of messages sent to a computer bulletin board is a Poisson random variable with a mean of 5 messages per hour. (a) What is the probability that 5 messages are received in 1 hour? (b) What is the probability that 10 messages are received in 1.5 hour? Engineering Statistics (c) What is the probability that less than two messages are received in one-half hour? Ans. (0.1755, 0.0858, 0.2873) Q5/ The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter. (a) What is the probability that there are two flaws in 1 square meter of (b) What is the probability that there is one flaw in 10 square meters of cloth? (c) What is the probability that there are no flaws in 20 square meters of cloth? (d) What is the probability that there are at least two flaws in 10 square meters th? of cloth? Ans. (0.0045, 0.3679, 0.1353,0.2642) Q6/ The number of failures for a cryogenics machine from contamination in biological samples is a Poisson random variable with a mean of 0.01 per 100 samples. (a) If the lab usually processes 500 samples per day, what is the expected number of failures per day? (b) What is the probability that the machine will not fail during a study that includes 500 participants? (assume one sample per participant.) Ans. (0.05, 0.9512)
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