Download (1) If X is a normal random variable with mean 80 and standard

Stat 2411
Spring 2007
Last Class
(1) If X is a normal random variable with mean 80 and standard deviation 10, compute
the following probabilities by standardizing:
(a) P( X  100)
(b) P(65  X  100)
(c) P(70  X )
(2) If measurements of the specific gravity of a metal can be looked upon as a random
sample from a normal population with the standard deviation =0.025 ounce, what is the
probability that the mean of a random sample of size n=16 will be off by at most 0.01
ounce?
(3) Suppose that the number of small aircraft arrivals at a certain airport follows a
Poisson distribution with λ=8 per hour.
(a) What is the probability that exactly 6 small aircraft arrive during a 1-hour period?
(b) What is the probability that at most 3 arrive during a ½ hour period?
(c) How many minutes do we need to wait to have a 90% chance of an airplane having
arrived?
(4) If 40% of the mice used in an experiment will become very aggressive within two
minutes after having been administered an experimental drug, find the probability that
exactly four of nine mice that have been administered the drug will become very
aggressive within two minutes.
(5) A collection of eight Spanish gold doubloons contains five counterfeits. If two of
these coins are randomly selected to be sold at auction, what are the probabilities that
(a) neither coin is a counterfeit;
(b) either or both coins are counterfeits?
(6) 1% of women at age forty who participate in routine screening have breast cancer.
80% of women with breast cancer will get positive mammographies. 9.6% of women
without breast cancer will also get positive mammographies. A woman in this age group
had a positive mammography in a routine screening. What is the probability that she
actually has breast cancer?
(7) A carton of 24 light bulbs includes two that are defective. If two of the bulbs are
chosen at random, what are the probabilities that
(a) neither bulb will be defective;
(b) one of the bulbs will be defective;
(c) both bulbs will be defective?
(8) A particular type of seed has a 0.50 probability of producing pink flowers. If we
grow 100 independent seeds, what is the probability we get 60 or more pink flowers?