Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 14
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20Exercises
1. The probability that a mountain-bike rider travelling along a certain track will have a tyre burst
is 0.05. Find the probability that among 17 riders:
(a) exactly one has a burst tyre
(b) at most three have a burst tyre
(c) two or more have burst tyres.
2. (a) A transmission channel transmits zeros and ones in strings of length 8, called ‘words’.
Possible distortion may change a one to a zero or vice versa; assume this distortion occurs
with probability .01 for each digit, independently. An error-correcting code is employed
in the construction of the word such that the receiver can deduce the word correctly if at
most one digit is in error. What is the probability the word is decoded incorrectly?
(b) Assume that a word is a sequence of 10 zeros or ones and, as before, the probability of
incorrect transmission of a digit is .01. If the error-correcting code allows correct decoding
of the word if no more than two digits are incorrect, compute the probability that the
word is decoded correctly.
3. An examination consists of 10 multi-choice questions, in each of which a candidate has to
deduce which one of five suggested answers is correct. A completely unprepared student
guesses each answer completely randomly. What is the probability that this student gets 8 or
more questions correct? Draw the appropriate moral!
4. The probability that a machine will produce all bolts in a production run within specification
is 0.998. A sample of 8 machines is taken at random. Calculate the probability that
(a) all 8 machines, (b) 7 or 8 machines, (c) at least 6 machines
will produce all bolts within specification
5. The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40
machines are selected at random, calculate the probability that 38 or more will not develop any
faults within the first 3 years of use.
6. A computer installation has 10 terminals. Independently, the probability that any one terminal
will require attention during a week is 0.1. Find the probabilities that
(a) 0, (b), 1 (c) 2, (d) 3 or more, terminals will require attention during the next week.
7. The quality of electronic chips is checked by examining samples of 5. The frequency distribution
of the number of defective chips per sample obtained when 100 samples have been examined
is:
No. of defectives 0
1
2
3 4 5
No. of samples
47 34 16 3 0 0
Calculate the proportion of defective chips in the 500 tested. Assuming that a binomial distri-
bution holds, use this value to calculate the expected frequencies corresponding to the observed
frequencies in the table.
30
HELM (2008):
Workbook 37: Discrete Probability Distributions
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