MAT 212 Probability and Statistics for Science &
Engineering
Autumn 2020: Class Test3
Time: 60 minutes
1. An experiment on breakdown voltage on diodes produced the following results.
7.84
8.06
5.70
7.02
7.16
9.01
8.92
7.78
5.93
5.79
8.89
7.60
7.67
8.94
5.28
8.46
7.74
6.07
5.43
8.16
6.87
6.00
8.42
6.19
6.80
8.87
5.50
7.33
6.04
6.51
a) Construct a frequency table from the above data using 8 class intervals.
(10 points)
b) Using the frequency table, calculate the mean and variance of the breakdown voltage
(10 points)
2. The number of surface flaws in plastic panels used in the interior of automobiles has a
Poisson distribution with a mean of 0.03 flaw per square foot of plastic panel. Assume an
automobile interior contains 8 square feet of plastic panel.
(a) What is the probability that there are no surface flaws in an auto’s interior?
(b) The company has a stock of 20 cars, of those it is known that 6 have defective interior
panels. If 8 cars are sold to a rental company what is the probability that at most one car
has any surface flaws?
(10 points)
3. The probability that your call to a service line is answered in less than 30 seconds is 0.75.
Assume that your calls are independent.
(a) If you call 10 times, what is the probability that exactly 8 of your calls are answered
within 30 seconds?
(b) If you call 20 times, what is the probability that at most 16 calls are answered in less
than 30 seconds?
(d) What is the probability that you must call six times to obtain the first answer in less
than 30 seconds?
(f) What is the probability that you must call eight times for three of your calls to be
answered in less than 30 seconds?
(20 points)
4. Magnetic tape is slit into half-inch widths that are wound into cartridges. A slitter assembly
contains 48 blades. eight blades are selected at random and evaluated each day for
sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set
of blades.
(a) If 12 of the blades in an assembly are dull, what is the probability that the assembly is
replaced the first day it is evaluated?
(b) If 12 of the blades in an assembly are dull, what is the probability that the assembly is
not replaced until the third day of evaluation?
(c) Suppose on the first day of evaluation, two of the blades are dull, on the second day of
evaluation six are dull, and on the third day of evaluation, ten are dull. What is the
probability that the assembly is not replaced until the third day of evaluation?
(5 + 5 + 10 points)
5. At a factory 20 parts are checked each hour and that X denotes the number of parts in the
sample of 20 that require rework. If the percentage of parts that require rework is 1%, what
is the probability that hour 10 is the first sample at which X exceeds 1?
(10 points)
6. Each main bearing cap in an engine contains four bolts. The bolts are selected at random,
without replacement, from a parts bin that contains 30 bolts from one supplier and 70 bolts
from another.
(a) What is the probability that a main bearing cap contains all bolts from the same
supplier?
(b) What is the probability that at least three bolts are from the same supplier?
(5 + 10 points)