1
The following represents the game time, in minutes, for the Major
League Baseball games played in the United States between March 30
and April 9, 2003, sorted by league. Compare the times between the
two leagues in terms of the average and the variability. A TV producer
wants to know, for purposes of scheduling her crew, what the chances
are that a game will end in 180 min. in each of the leagues. She also
wants to know the time before which 95% of the games will end in
each league? (Data based on report by Garrett 2003.)
American League
174 125 130 155 170 225 159 315 143 147 160 173 178 178 194 120 202
143 146 149 179 181 183 185 175 161 169 179 188 193 200 156 161 197
145 162 167 172 179 181 134 174 203 222 174 188 176 231 176 131 126
National League
164 171 174 180 183 197 209 149 150 153 214 146 142 155 136 150 154 170
155 162 164 173 179 208 156 164 166 169 161 169 172 177 201 278 135 172
171 173 188 133 162 163 163 190 195 197 169 172 178 209 182 237 151 178
2
A high-rise tower built by a developer contains 200 condominium
units. The QA department of the developer has to approve the tower
before turning it over to sales. The QA department will select a random
sample of 8 units and inspect them. If more than three major
defects are found in any unit, they will reject the unit as defective. If
more than 2 of the 8 inspected units are defective, the entire tower
will be rejected. If 10 of the 200 units are known to have more than
three major defects, what is the probability that the tower will be
rejected?
3
A plane has four engines. Each engine has a probability of failing
during a flight of 0.3. What is the probability that no more than
two engines will fail during a flight? Assume that the engines are
independent.
4
The thickness of gear blanks produced by an automatic lathe is
known to be normally distributed, with a mean of 0.5 in. and a standard
deviation of 0.05 in. If 10% of the blanks are rejected for being
too thin, where is the lower specification located?
5
Automatic fillers are used to fill cans of cooking oil, which have to
meet a minimum specification of 10 oz. To ensure that every can
meets this minimum, the company has set a target value for the process
average at 11 oz. The standard deviation of the amount of oil in
a can is known to be 0.20 oz.
a. At the process average of 11 oz, what percentage of the cans will
contain less than 10 oz of cooking oil? Assume that the amount
of oil in cans is normally distributed.
b. Assuming that virtually all values of a normal distribution fall
within a distance of 3.5σ from the mean, find the minimum value
to which the process average can be lowered so that virtually no
can will have less than 10 oz?
6
A random sample of nine electric bulbs was chosen from a production
process and tested until failure. The lives in hours were 1366, 1372, 1430, 1246, 1449,
1268, 1408, 1468, and 1502, respectively. Give a
95% CI for the average life of the bulbs produced in the process if it is
known that the life is normally distributed with a standard deviation
of 100 hours.
7
A random sample of nine electric bulbs was chosen from a production
process and tested until failure. The lives in hours were 1366,
1372, 1430, 1246, 1449, 1268, 1408, 1468, and 1502, respectively. Give a
90% CI for the mean life of the bulbs produced in the process if it is
known that the life is normally distributed but the population standard
deviation is not known.
8
The shelf life of a battery is of interest to a manufacturer. A random
sample of 10 batteries gave the following shelf lives in days: 108, 122,
110, 138, 124, 163, 124, 159, 106, and 134. Is there evidence that the
mean shelf life is greater than 125 days? Assume that the shelf life is
normal. Use α = 0.05.
9
A survey of alumni of two engineering programs in a college gave
the following data on their salaries after five years. Is there evidence
to show that the average salaries of the graduates from the
two programs are different? Assume that both the salaries are normally
distributed and have a standard deviation of $12,000. Use
α = 0.10.
IE Graduates
ME Graduates
66,500
64,600
58,200
58,900
80,400
76,900
48,500
45,800
64,500
70,100
68,300
69,700
77,300
77,900
84,900
52,300
...

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