Download test 2 review problems

Mathematics 109 second test review problems
1. Use a calculator or the table for the standard normal distribution to calculate:
(a) 15!
(b)
12 C3
(c) P (z < 0.72) =
(d) P (z <
) = 0.35
2. How many re-arrangements of the letters SU RGE are possible? of ST AT IST ICS ?
3. How many different 12-person juries can be drawn from a jury pool of 42 persons?
4. Suppose that a large class has normally distributed test scores, with a mean test score
of 75 and a standard deviation of 6. What test score corresponds to the 90th percentile?
5. Suppose in a certain population that the event R of being rich and the event S of
being smart are independent events. What is the probability of being rich and smart if
P (R) = 0.05 and P (S) = 0.02.
6. Suppose in a certain population that the event R of being rich and the event S of being
smart are mutually exclusive. What is the probability of being rich or smart if P (R) = 0.05
and P (S) = 0.02.
7. Determine whether each of the following is or is not a possible probability distribution:
value
value
probability
probability
value
probability
x = 0 P (x = 0) = 0.4
x = 0 P (x = 0) = 0.4
(a) x = 0 P (x = 0) = 0.2 (b)
(c)
x = 1 P (x = 1) = 0.9
x = 2 P (x = 2) = 0.5
x = 1 P (x = 1) = 0.8
x = 2 P (x = 2) = −0.3
x = 4 P (x = 4) = 0.2
8. Suppose that the probability of a successful plastic surgery operation is 80%. For a
person who has had ten plastic surgery operations, compute the probability that
• all operations are successful
• exactly eight of the ten operations are successful
• at most eight operations are successful
9. Suppose the heights of young adult males in a distant country are normally distributed,
with a mean of 168 cm, with a standard deviation of 8 cm.
Suppose that all possible samples of 100 young adult males are drawn randomly out of the
population of this country, and the mean height is calculated for each sample.
• what is the mean of all the sample means?
• what is the standard deviation of the sample means?
• what is the probability that a sample mean is greater than 169 cm?
page two
10. A group of 10, 000 trees in a forest is studied. It turns out that 3000 of the trees are
pine trees, 2000 of the trees are sick, and that 1500 of the trees are pine trees and are sick.
If trees are randomly selected from this group, let P IN E be the event that a pine tree is
selected, and let SICK be the event that a sick tree is selected. Compute the probabilities:
(a) P (SICK)
(b) the conditional probability P (SICK | P IN E)
(c) P (SICK or P IN E)
11. A set of measurements of the length of an infant is normally distribued, with a mean of
21 inches, and a standard deviation of 0.4 inches.
• calculate the probability that a measurement is between 20.8 and 21.4 inches.
• find the length of an infant who is in the 85th percentile for length.
12. If I draw five cards from a 52 card deck (with no replacement), calculate the probabilities
that
• exactly three of the cards have the same suit
• exactly two of the cards have the same number (or face)
• the probability that the last two cards I draw are spades, given the fact that the first
three cards I drew were hearts.