Practice Midterm II

Printable Key

Problem 1

The South Lake Tahoe Police Department has charted the number of arrests over the past twelve months.  The number of arrests per month that are made follows a Normal distribution with mean 72 and standard deviation 12.  Construct a control chart and determine any out of control signals.

Solution

Problem 2

Stellar Jay hatchlings have a body weight that is approximately normally distributed with a mean of 3.4 ounces and a standard deviation of 0.3 ounces.  

A.  Convert the following x-intervals into z-intervals.

            x > 3.0                        x < 6.0

Solution

B.  Convert the following z-interval into an x-interval

            -1.2 < z < 0.6            

Solution

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?

Solution

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?

Solution

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.  What is the probability that between 20 and 25 of the rooms host bay area visitors?

Solution

B.  Why is your estimate valid?

Solution

Problem 5

 Explain what the difference is between a sampling distribution and the distribution of a sample.

Solution

Problem 6

It is know 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?

Solution

B.  25 children were randomly selected and observed.  What is the probability that their mean number of visits is between 48 and 55?

Solution

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?

Solution

B.  Is the normal approximation to the proportion p = r/n valid?  Explain.

Solution

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.  Construct a 95% confidence interval for the true mean.  Write a sentence that explains your findings.

Solution

Problem 9

Thirteen brown 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 brown bears in the Sierra Nevada Mountains.

Solution

B.  What assumption do you need for your answer in part A to be valid?

Solution

C.  Write a sentence that explains your findings.

Solution

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.  Construct a 90% confidence interval for the true proportion of people who will refuse to zap the animal.  Write a sentence that explains your findings.

Solution

Problem 11

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%?

Solution

Problem 12

A study was done to compare the pass rates of Caucasians and Latinos in their statistics class.  192 Caucasians and 83 Latinos were considered.  135 of the Caucasians and 70 of the Latinos passed the course.  Find a 95% confidence interval for p₁ - p₂  and explain in a complete sentence what it means.

Solution