1. Mercury Mufflers guarantees its muffler for 3 years. On each
muffler, they make a profit of $15. However, they must pay $50
for any replacement under the guarantee. If this replacement
also burns out within 3 years, they are not committed to a
second replacement). They muffler life is approximately
normally distributed around a mean of 4.2 years, with a
standard deviation of 1.8 years.
(a). What is the average net profit per sale (that is, profit
the cost of possible replacement)
(b). If they want this average profit per sale to be $5, by
how much should they reduce the time period of the
guarantee?
2. In Boston in 1968, Dr. Benjamin Spock, a famous
pediatrician and activist against the Vietnamese was, was tried
for conspiracy to violate the Selective Service Act (Military
Draft). The judge who tried Dr. Spock had the following
interesting record. Of the 700 people the judge had selected for
jury duty in his previous trials, only 15% were women. Yet in
the city as a whole, about 29%of the eligible jurors were
women. Let p denote the probability that a juror drawn by the
judge is a woman. Then to test the judge’s fairness in selecting
women, what null hypothesis should be? What alternative
hypothesis should be?
3. A manufacturer needs washers between 0.1180 and 0.1220
inches thick; any thickness outside this range is unusable. One
machine shop will sell washers at $3.00 per 1000 washers.
Their thickness is normally distributed with a mean ofo. 1200
and a standard deviation of 0.0010 inch. A second shop will sell
washers at $2.60 per 1000. Their thickness is normally
distributed with a mean of 0.1200 inch and a standard deviation
of 0.001 5 inch. Which shop offers the better deal?
4. Suppose a large class in statistics has marks normally
distributed around a mean of 72 with a standard deviation of 9.
Find the following:
a. The probability that an individual student drawn at random
will have a mark over 80.
b. The probability that a random sample of 30 students will
have an average mark over 80.
c. If the population were not normal, what would be your
answer to part b?
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