Exam 2
Name:
Fall 2015. Math 2500
Show all your works. No credits for guessing.
1. Suppose 25% of the trees in a forest have severe leaf damage from air pollution.
If 20 trees are selected at random, find the probability that:
(a) No more than two have severe leaf damage.
(b) No less than 19 trees have severe leaf damage.
2. The probability that a student is accepted to a prestigious college is 0.3. If 5
students from the same school apply, what is the probability that at most 2 are
accepted?
3. A poison distribution with the mean 2 governs the daily number of insurance
handled by an adjuster. Determine the probability that she handles
(a) No claims tomorrow.
(b) 15 claims in the next week.
(c) No more than one claims tomorrow.
4. The number of weekly breakdowns of a department’s computing system is a
random variable having a Poisson distribution with the mean 0.5. What is the
probability the computer will run for two consecutive weeks without breakdowns?
5. The weights of apples served at a restaurant are normally distributed with a mean
of 6 ounces and standard deviation of 1.2 ounces. What is the probability that the
next person served will be given an apple that weighs less than 5 ounces?
6. The time it takes a symphony orchestra to play Beethoven’s Ninth Symphony has
a normal distribution with a mean of 64.5 minutes and a standard deviation of 1.5
minutes. The next time it is played, what is the probability that it will take between
61.5 and 68.5 minutes?
7. Suppose the weights of the contents of cans of mixed nuts have a normal
distribution with mean 32.5 ounces and standard deviation .5 ounce.
(a) If every can is labeled 31 ounces, what proportion of the cans have contents that
weigh less than the labeled amount?
(b) If two packages are randomly selected, specify the mean, standard deviation, and
distribution of the average weight of the contents.
(c) If four packages are randomly selected, what is the probability that the average
weight is less than 32 ounces?
8. Lightning causes many deaths each year in the United States. One plausible model
for the population distribution of the number of death per year has mean 70 and
standard deviation 38 deaths per year. Calculate the mean and standard deviation of
for a random sample of size
(a) 4
(b) 25.