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10.  At a factory that produces pistons for cars, Machine 1 produced satisfactory pistons and unsatisfactory pistons today. Machine 2 produced satisfactory pistons and unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today’s batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory ?

 

11. A survey showed that 23% of college students read newspapers on a regular basis and that 81% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.

 

    (a) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.

 

    (b) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to decimal places.

A=

B=

 

13. Let be a random variable with the following probability distribution:

Value x of X             P(X=x)

10                                 .10

20                                  .65

30                                  .10

40                                  .05

50                                  .10

 

E(x)=

Var(X)=

 

14. Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of 20 Colonials games.

 

    Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

 

    Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

a. ­­­___

b. ___

 

15. A study of college football games shows that the number of holding penalties assessed has a mean of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?1%2D1penalties per game and a standard deviation of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?3%2D%3Bpenalties per game. What is the probability that, for a sample of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?73college games to be played next week, the mean number of holding penalties will be https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?1%2D2penalties per game or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

______

16. Let https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?Ybe a standard normal random variable. Use the calculator provided to determine the value of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%60such that

https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?S%23%2B%2E%60%23%25of%23Y%23%25of%23%60%2A%23%3E%233%2D%3A7%3B%3B.

 

17. The union for a particular industry has determined that the standard deviation of the daily wages of its workers is $https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?16 . A random sample of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%3B3workers in this industry has a mean daily wage of $https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?211 . Find a https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%3A6%26confidence interval for the true mean daily wage of all union workers in the industry. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

What is the lower limit of the 95% confidence interval?

What is the upper limit of the 95% confidence interval?

18. ·  Consider a t distribution with https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%3Adegrees of freedom. Compute https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?S%23%2Bw%23%25df%232%2D64%2A. Round your answer to at least three decimal places.

·  Consider a t distribution with https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?03degrees of freedom. Find the value of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%60such that https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?S%23%2B%2E%60%23%25ow%23w%23%25ow%23%60%2A%23%3E%233%2D%3A3. Round your answer to at least three decimal places.

=

C=

 

  • 19. Suppose that https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25hkj%3Fpvs%3D1%3F%2Cpvs%3Dfollows a chi-square distribution with https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?16degrees of freedom. Compute https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?S%2B25%23%25of%23%25hkj%3Fpvs%3D1%3F%2Cpvs%3D%23%25of%230%3B%2A. Round your answer to at least three decimal places.
  • Suppose again that https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25hkj%3Fpvs%3D1%3F%2Cpvs%3Dfollows a chi-square distribution with https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?16degrees of freedom. Find https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?hsuch that https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?S%2B%25hkj%3Fpvs%3D1%3F%2Cpvs%3D%23%25dw%23h%2A%23%3E%233%2D316. Round your answer to at least two decimal places.
  • Find the median of the chi-square distribution with https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?16degrees of freedom. Round your answer to at least two decimal places.

P=

K=

Median=

20. The records of a casualty insurance company show that, in the past, its clients have had a mean of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?2%2D%3Bauto accidents per day with a standard deviation of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?3%2D36. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?3%2D36. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries’ claim. State the null hypothesis https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?K%3Fpva%3D3%3F%2Cpva%3Dand the alternative hypothesis https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?K%3Fpva%3D2%3F%2Cpva%3Dthat we would use for this test.

Ho=

H1=

 

21. A laboratory claims that the mean sodium level, https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25nv8, of a healthy adult is https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?273mEq per liter of blood. To test this claim, a random sample of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?72adult patients is evaluated. The mean sodium level for the sample is https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?277mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?23mEq. Assume that the population is normally distributed. Can we conclude, at the https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?3%2D2level of significance, that the population mean adult sodium level differs from that claimed by the laboratory?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

Ho=

H1=

The type of test statics=Z,T,F OR Chi square

The value=

The two critical values

Can we could the population mean           yes or no

 

22. For a study conducted by the research department of a pharmaceutical company, https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?106randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication. The sample mean was found to be https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%2724%2D43with a standard deviation of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%277%2D%3A3. A random sample of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?116individuals was selected independently of the first sample. These individuals reported their annual spending on non-prescription allergy relief medication. The mean of the second sample was found to be https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%272%3B%2D03with a standard deviation of https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%270%2D73. As the sample sizes were quite large, it was assumed that the respective population standard deviations of the spending for prescription and non-prescription allergy relief medication could be estimated as the respective sample standard deviation values given above. Construct a https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%3A3%26confidence interval for the difference https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25nv8%3Fpva%3D2%3F%2Cpva%3D%23%2E%23%25nv8%3Fpva%3D1%3F%2Cpva%3Dbetween the mean spending on prescription allergy relief medication (https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25nv%3Fpva%3D2%3F%2Cpva%3D) and the mean spending on non-prescription allergy relief medication (https://secure.aleks.com/alekscgi/x/math2htgif.exe/NM?%25nv%3Fpva%3D1%3F%2Cpva%3D). Then complete the table below

What is the lower limit 90%

What is the upper limit of 90%

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