Download Math146 Midterm Sum12

North Seattle Community College
Summer 2012
MATH 146 Elementary Statistics
Midterm
NAME: _______________________
July 30th, 2012
SCORE: ______________________
Question 1 (7 points):
I. As of January 2010, there were 755 “ oldies” radio stations in the United States. If one
station finds that 104 stations have a larger daily audience than it has, what percentile
does this station come closest to in the daily audience rankings?
II. A batch of 200 calculators contains 3 defective units. What is the probability that a
sample of three calculators will have
(a) no defective calculators?
(b) all defective calculators?
(c) at least one defective calculator?
(d) at least one non-defective calculator?
Question 2 (10 points):
The table shows the number (in thousands) of earned degrees, by level and gender,
conferred in the United States in a recent year.
A person who earned a degree in the year is randomly selected. Find the probability of
selecting someone who
(a) earned a bachelor’s degree.
(b) earned a bachelor’s degree given that the person is a female.
(c) earned a bachelor’s degree given that the person is not a female.
(d) earned an associate’s degree or a bachelor’s degree.
(e) earned a doctorate given that the person is a male.
(f) earned a master’s degree or is a female.
(g) earned an associate’s degree and is a male.
(h) is a female given that the person earned a bachelor’s degree.
Are gender and level of degree independent? Explain.
Question 3 (6 points):
Basketball player Dwight Howard makes a free throw shot about 60.2% of the time.
(a) Find the probability that the first free throw shot Dwight makes is the fourth
shot. Is this an unusual event? Explain.
(b) Find the probability that the first free throw shot Dwight makes is the second or
third shot. Is this an unusual event? Explain.
Question 4 (7 points):
The per capita consumption of red meat by people in the United States in a recent year
was normally distributed, with a mean of 108.3 pounds and a standard deviation of 35.1
pounds. Random samples of 40 people are drawn from this population and the mean of
each sample is determined. Use the Central Limit Theorem to find the mean and
standard error of the mean of the indicated sampling distribution. Then sketch a graph
of the sampling distribution.
Question 5
I. (10 points)
A study found that the mean migration distance of the green turtle was 2200 kilometers
and the standard deviation was 625 kilometers. Assuming that the distances are
normally distributed, find the probability that a randomly selected green turtle migrates
a distance of
(a) less than 1900 kilometers.
(b) between 2000 kilometers and 2500 kilometers.
(c) greater than 2450 kilometers.
II. (10 points)
A sample of 12 green turtles is randomly selected. Use central limit theorem to find the
distribution, mean and standard error of the sampling distribution of sample means.
Also find the probability that the sample mean of the distance migrated is
(a) less than 1900 kilometers,
(b) between 2000 kilometers and 2500 kilometers, and
(c) greater than 2450 kilometers.