i need help with this stats qoustions
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practice_test2.zipMATH 200 ReviewTEST 2.docx
Math 200 Midterm II Spring 2014 Good luck to: --------------------------------------------
Note : There are 10 problems on this exam (10pts each). Use of calculators to check your work is permitted; however, in order to receive full credit for any problem, you must show all relevant work leading to your answer. You have 120 minutes to complete this test.
1. There is a 0.9986 probability that a randomly selected 30-year -old male lives through the year. A fidelity life insurance company charges $161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit.
a. If a 30-year-old male purchases the policy, what is his expected value?
b. Can the insurance company expect to make a profit from many such policies? Why?
2. Draw a picture and show work for full credit. Assume that is a standard normal variable.
a. If, find .
b. Find the indicted value
3. Assuming that Men’s heights are normally distributed with mean 69.0 in. and standard deviation 2.8 in and Women’s heights are normally distributed with mean 63.6. and standard deviation 2.5 in.
The Mark VI monorail used at Disney World and the Boeing 757-200 ER airline have doors with a height of 72 in.
a. What percentage of adult men can fit through the doors without bending
b. What percentage of adult women can fit through the doors without bending?
c. What doorway height would allow 98% of adult men to fit without bending
4. Currently, quarters have weights that are normally distributed with a mean of 5.670 g and standard deviation of 0.062 g. a vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.
a. If 280 different quarters are inserted into the vending machine, what is the expected number of rejected quarters?
b. If 280 different quarters are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.550 g and 5.790 g?
c. If you own the vending machine, which result would concern you more? The result from part (a) or the result from part (b)? Why?
5. In a poll of 600 randomly selected subjects, 200 answered “yes” when asked if they planned to vote in a state election.
a. What is the best point estimate of the population proportion of all who plan to vote in that election?
b. Construct a 95% confidence interval estimate of the proportion of all who plan to vote in that election.
c. Interpret this interval.
6. When 14 different second-year medical students at Bellevue Hospital measured the blood pressure of the same person, they obtained the results listed below:
138, 130, 135, 140, 120, 125, 120, 130, 130, 144, 143, 140, 130, 150
Assuming that the population standard deviation is known to be 10 mmHg.
a. Construct a 95% confidence interval estimate for the population mean.
b. Interpret this interval.
7. Listed below are 12 lengths (in minutes) of randomly selected movies.
110, 96, 125, 94, 132, 120, 136, 154, 149, 94, 119, 132
a. Construct a confidence interval estimate for the mean length of all movies.
b. Interpret this interval.
8. Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes.
a. What is the probability that a customer will spend more than 15 minutes in the bank?
b. What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes?
9. Company provides electricity with voltage levels between 123.0 volts and 125.0 volts. That is, any voltage amount between 124.0 volts and 126.0 volts is possible, and all the possible values are equally likely.
a. Find the probability that a randomly selected voltage level is greater than 123.8 volts. Support your answer with a graph of the distribution.
b. Find the 95th percentile.
10. Doorway Height. The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of2.8 in.
a. If a male passenger is normally selected, find the probability that he can fit through the doorway without bending. (Support your answer with a graph).
b. If half of the 200passengers are men, find the probability that the mean height of 100 men is less than 72 in. (Support your answer with a graph).
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?
d. When considering the comfort and safety of passengers, why are women ignored in this case?
