MAT 107 Test #2
NAME:
Directions: Read and answer each question carefully. Do NOT remove the staple! Use
backs of pages if necessary. Show all work! Probabilities should be carried out to 3
decimal places or left as fractions. Circle or box your answers!
1. A recent study at a New England university found that 60% of all students missed
class during the semester because of drinking. A random sample of 20 students is
taken. Find the probability more than 15 students missed class because of
drinking? Find the probability less than 5 students missed class because of
drinking? Find the probability between 5 and 15 (inclusive) students missed class
because of drinking. What are the mean and standard deviation of the number of
students who missed class because of drinking from the sample.
2. Consider the following data from the study on binge drinking, about number of
hangovers per semester. Find the probability that a randomly selected student:
a.
Is male.
b.
Is both female and had no hangovers
c.
Had a hangover twice or more, given she is female.
d.
Is male, given he had only one hangover.
e.
Are being Male and having one hangover independent?
Gender
Male
Female
Number
None
61
66
Of
One
23
25
Hangovers
Two or More
40
36
3. The weight of 18 year old males in Anchorage, Alaska is normally distributed
with mean 175 lbs and a standard deviation 30 lbs. A randomly selected 18 year
old male from Anchorage is selected. What is the probability he weighs less than
137 lbs? What is the probability he weighs more than 215 lbs? What is the
probability he weighs between 137 lbs and 200 lbs? Find the weight, w, such that
only 10% of the males from Anchorage weigh more than w.
4. A casino devises a new game such that your winnings based on a $5 bet are given
by the probability distribution below, where x is your winnings. You bet $5. What
is probability you win $5? What is the probability you do not win $10? What is
the probability you do not lose money? What are your expected (mean) winnings?
X
p(x)
-5
0.40
0
0.25
5
?
10
0.10
Answers:
1. P( X > 15) = 0.050, P( X < 5) = 0.000, P(5 <= X <=15) = 0.949
μ = 20 * .6 = 12, σ = sqrt( 20* .6 * .4) = 2.191
2. P(male) = 124/251, P(female ∩ None) = 66/251
P(Twice | Female) = 36/127, P(Male | One) = 23/48
Male and One are not independent, P(male) * P(one) not = P(male ∩one)
P(one) = 48/251, P(male) * P(one) = .094, P(male ∩one) = .092
3. P( X < 137) = P( Z < -1.27) = .1020
P( X > 215) = P( Z > 1.33) = .0918
P(137 < X < 200) = P(Z < 0.83) – P(Z < -1.27) = .7967 - .1020 = .6947
P( Z > 1.28) = .10, w = 1.28*30 + 175 = 213.4
4. P(X = 5) = .25
P((X = 10)’ ) = 1 - .10 = .90
P(X >= 0) = 1 - .40 = .60
E(X) = -5*.40 + 0*.25 + 5*.25 + 10*.10 = .25