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University of Maryland
University College
Stat 200 Quiz
2 â 80 points
This is an open-book, open-notes
quiz. A calculator, Excel or other software may be used and are encouraged. You
may add spaces as needed to show your work. You must show your work OR cite your calculator
app or website app to receive full credit. An answer that consists of simply a
number will receive no credit.
1. (5 pts) A bag contains 5 white, 10
blue, 12 red, 7 yellow, and 6 green candies. A candy is selected from the bag
and kept. You then draw a second candy and keep it also. What is the
probability of selecting 2 green candies? Leave the answers in fractional form.
2. (9 pts) A person wins in a gambling
game if he gets 2 heads in 5 flips of a biased coin. The probability of getting
a head is 0.7. a) Find the probability
that he wins. Should he play? b) If the
rules change and he wins if he gets at least 4 heads in 5 flips, what is the probability
that he wins?
3.
(4
pts) A life insurance company sells a $250,000 1-year term life insurance
policy to a 20-year-old female for $200. According to the National Vital
Statistics Report, 58(21), the probability that the female survives the year is
0.999544. What is the expected cost of the insurance policy to the 20-year-old
female buyer?
4.
(6
pts) There is a probability of 0.05 that a lamp purchased at a given store
doesnât work. A person purchases 3 lamps. a) Define a random variable as the
number of non-working lamps. What is the sample space? b) Find the probability
distribution.
5. (6 pts) Flight 215 from Orlando to Los
Angeles is on time 90% of the time. Randomly select
150 flights from Orlando to Los Angeles and use the normal approximation
to the binomial to approximate the probability that exactly 130 flights are on
time. Compare it with the probability calculated using the binomial
distribution.
6. (8 pts) The tread life of a
particular brand of tire is a random variable
described by a normal distribution with a mean of 65,000 miles and a
standard deviation of 2500 miles. What is the probability a particular tire of
this brand will last longer than 57,400 miles? What percentage of tires will last between
50,000 miles and 70,000 miles?
7. (4 pts) The time spent in the
drive-thru at Wendyâs is normally distributed with a mean of 138.5 seconds and
a standard deviation of 29 seconds. Wendyâs wants to initiate a policy that it
will not charge any patron who has to wait more than a certain amount of time
for an order in the drive-thru. Management does not want to give away free meals
to more than 1% of the patrons. What time would you recommend Wendyâs advertise
as the maximum wait time before a free meal is awarded? Wendyâs has no way to
measure fractions of seconds so your answer should be a whole number.
8. (4 pts) The amount of corn chips
dispensed into a 13-ounce bag by the dispensing machine has been identified as
possessing a normal distribution with a mean of 13.5 ounces and a standard
deviation of 0.1 ounce. Suppose 100 bags of chips were randomly selected from
this dispensing machine. Find the probability that the sample mean weight of
these 100 bags exceeded 13.55 ounces.
