Use the following information to answer questions 1 and 2.
In a sample of 240 undergraduates, of the males 80 were in the College of Arts and Sciences, 40 were in the College of Business, and 10 were in the College of Engineering. For the females, 60 were in the College of Arts and Sciences, 16 were in the College of Business, and 34 were in the College of Engineering.
__________1. ) If one student is randomly selected, find the probability that the
student is a male in the College of Business.
__________2. ) If one student is randomly selected, find the probability that the
student is in the College of Business given that she is female.
__________3. ) The probability that a first-time tourist to the city of Chicago will visit the Art Institute is 0.4, will visit the Museum of Science and Industry is 0.3, and will visit both is 0.1. If a first-time tourist to Chicago is randomly selected, find the probability that the tourist will visit the Art Institute or the Museum of Science and Industry.
__________4. ) Events A, B and C are events of a
sample space, S, with A and C mutually exclusive, B and C mutually exclusive,
P(A)=0.32, P(B)=0.11, P(A
B)=0.08, and P(C)=0.42.
Find the 
.
_________5. ) Twenty percent of the trees in a particular forest have a disease,
30 % of the trees are too small to be used for lumber, and 40% are too small to be used for lumber or have a disease. What percent of the tree are too small to be used for lumber and have a disease? ( 6 points )
Use the following information to answer questions 6 and 7.
A card is selected from a standard deck of 52. Random variable x is defined to be 0, if an ace occurs; 1, if a two through ten occurs; and 2, if a face card ( Jack, Queen, or King ) occurs.
6. ) Give the probability distribution for x. ( 6 points )
x p(x)
_________7. ) Find the mean of the probability distribution in question 6.
_________8. ) Sixty percent of the applicants at a high tech firm have a college degree, 40% have at least three years experience in the high tech industry, and 35% have both a college degree and three years experience in the high tech industry. If an applicant is randomly chosen, find the probability that the applicant has a college degree or has had at least three years of experience in the high tech industry. ( 6 points )
_________9. ) A box contains five red, three blue, and two white poker chips. Two are selected without replacement. Find the probability that both are the same color. ( 6 points )
________10. ) Thirty percent of hospital admissions for diabetic patients are related to problems with the kidneys. In a sample of 10 diabetic hospital admissions, what is the probability that none will be for a kidney problem?
( 6 points )
_________11. ) Find the probability of a randomly selected piece of data from a normal population will have a z-score between 0 and 1.25.
________12. ) A traffic study at one point on an interstate highway shows that vehicle speeds are normally distributed with a mean of 61.3 mph and a standard deviation of 3.3 mph. If a vehicle is randomly checked, find the probability that its speed is between 55.0 mph and 60.0 mph. ( 6 points )
_________13. ) What is the value for z(0.67)?
_________14. ) Find z(0.030) - z(0.74) .
_________15. ) Use the normal approximation of the binomial distribution to find
the probability of obtaining at least 60 heads when a coin is flipped 100 times. ( 6 points )
Use the following information to answer questions 16 –18.
Samples of size 50 are selected from test scores on a statistics exam. The test scores have a normal distribution with a mean of 78.1 and a standard deviation of 16.2.
________16. ) Find the probability that a single test score will be between 71.1 and 85.1. ( 6 points )
________17. ) Find the probability that the sample mean will be between 71.1 and 85.1. ( 6 points )
________18. ) Find the probability that a single test score will be equal to 85.
( 6 points )