Practice Exam II
Problem 1 Please answer the following True or False
To view a plethora of these problems, please go to the link below and check "Probability" and "Confidence Intervals and Z".
http://www.ltcconline.net/greenl/java/Statistics/TrueFalse/statTrueFalseWithChoices2.html
Problem 2 Five percent of all university students are math majors.
A. If 80 randomly selected college students are surveyed, what is the exact probability that at least 6 of them will be math majors.
B. Could you have used the normal distribution to approximate the binomial distribution for part A.
Problem 3
Your tire company's snow and mud tires have an average lifetime of 80,000 miles with a standard deviation of 10,000 miles. Answer the following assuming the distribution is normal.
A. If the current guarantee for the tires is 65,000 miles, about what percentage of the tires will wear out before the guarantee expires?
B. You want to reconsider the guarantee so that about 98% last past the guarantee period. What should you set as the guarantee period on your tires?
Problem 4
The Lake Tahoe Visitor's Authority has determined that 65% of the tourists who come to the Lake Tahoe area to go snowboarding are from the Bay area. The Boarder Motel has all of its 35 rooms booked during this weekend.
A. Use the normal distribution to estimate the probability that between 20 and 25 of the rooms host bay area visitors?
B. Why is your estimate valid?
Problem 5
Explain what the difference is between a sampling distribution and the distribution of a sample.
Problem 6
It is known that the mean number of houses a Trick-Or-Treater visits is 46 and the standard deviation is 8.
A. Assuming that the distribution is approximately normal, what is the probability that your seven year old neighbor will visit fewer than 42 houses on Halloween?
B. 25 children were randomly selected and observed. What is the probability that their mean number of visits is between 48 and 55?
Problem 7
Do you favor allowing pilots to carry a gun in the cockpit? 74% of Americans are in favor of allowing pilots to carry a gun in the cockpit.
A. 80 passengers board a plane heading toward New York. What is the probability that the greater than 75% of them favor allowing the pilot to carry a gun? Use the normal approximation to work this problem out.
B. Is the normal approximation valid? Explain.
Problem 8
The manager of Wasabi restaurant tallied the number of customers that he received over a 50 day period. He found that the mean number per day for this period was 45 with a standard deviation of 8.
A. Construct a 95% confidence interval for the true mean.
B. Write a sentence that explains your findings.
C. Explain what it means in the context of this study to be 95% confident.
D. Was it necessary to make any assumptions about the underlying distribution of the population? Explain.
Problem 9
Thirteen black bears in the Sierra Nevada Mountains were captured and released for a research project. Their mean weight was found to be 320 pounds with a standard deviation of 23 pounds.
A. Determine a 95% confidence interval for the mean weight of black bears in the Sierra Nevada Mountains.
B. Write a sentence that explains your findings.
C. Explain what it means in the context of this study to be 95% confident.
D. Was it necessary to make any assumptions about the underlying distribution of the population? Explain.
Problem 10
A psychologist is doing research on blindly following orders. 200 volunteers were ordered to push a button that would inflict 50 volts of electricity into a laboratory animal. 35 of them refused to push the button.
A. Construct a 90% confidence interval for the true proportion of people who will refuse to zap the animal.
B. Write a sentence that explains your findings.
C. Explain what it means in the context of this study to be 95% confident.
D. Was it necessary to make any assumptions about the underlying distribution of the population? Explain.
Problem 11
Nationally, 2% of the population carry a venereal
disease. You are interested in constructing a 95%
confidence interval for the proprotion of carriers in the Tahoe Basin.
How many people will you need to test if you want a margin of error of
1%?
Problem 12
Your burger joint just sent out a coupon for fifty cent burgers. Your research has shown that 20% of coupon bearing customers just purchase a burger resulting a a loss to your restaurant of $0.25, 30% of coupon bearing customers also purchase fries with their burger resulting in a profit of $.50, and the rest opt for the full meal of a burger fries and a drink resulting in a profit of $1.50.
A. Write down a probability distribution table for the indicated distribution.
B. Find the expected value and standard deviation.
C. Use a complete sentence to interpret the expected value in the context of the question.