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 only "Confidence Intervals and Z" .
http://www.ltcconline.net/greenl/java/Statistics/TrueFalse/statTrueFalseWithChoices2.html
Problem 2
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 3
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 4
Explain what the difference is between a sampling distribution and the distribution of a sample.
Problem 5
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?
C. What is the probability that these 25 children visit a total of more than 1100 houses on Halloween?
Problem 6
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 7
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 90% confident.
D. Was it necessary to make any assumptions about the underlying distribution of the population? Explain.
Problem 8
Nationally, 2% of the population carry a venereal
disease. You are interested in constructing a 95%
confidence interval for the mean number of carriers in the Tahoe Basin.
How many people will you need to test if you want a margin of error of
1%?
Problem 9
The amount of fuel that is used in a day by a pizza delivery person is uniformly distributed between 1.5 and 12 gallons.
A. Write down the distribution.
B. Find the probability that on a randomly selected day the delivery person will use between 5 and 10 gallons.
C. Find the probability that on a randomly selected day the delivery person will use between more than 5 gallons given that less than 10 gallons was used.
D. Find the probability that the average fuel use on 45 days will be less than 6 gallons.