STAT 101 NCCU Permutations and Combinations Problems

Please do this problem by hand. Answers given by the calculator function will not get fullcredit.

7. The average TV viewing time per week for children ages 2 to 11 is 22.5 hours and thestandard deviation is 5.5 hours. Assume the viewing times are normally distributed, answerparts (a) – (e) below.**Show:

• Formulas

• Pictures

• calculations

• use Table II

-Standard Normal Table.

Final answers should be rounded to the nearest tenth.

7a) What percent of the children have viewing times less than 10 hours per week? (2)

7b) What percent of the children have viewing times between 15 and 25 hours per week? (2)

7c) How many hours of TV viewing cuts off the top 25% of the data?

(2)7d) How many hours of TV viewing cuts off the 90th percentile? (2)

8. The mean age of the nonresidential buildings is 30 years and the standard deviation of theages of nonresidential buildings is 5 years. The distribution of the ages is not normallydistributed.

8a) Calculate the standard error for the distribution of the means of the samples from thedistribution of ages of nonresidential buildings for sample sizes n = 50. Answers should berounded to the nearest hundredth. (1)____________________________________

8b) Calculate the standard error for the distribution of the means of the samples from thedistribution of ages of nonresidential buildings for sample sizes n = 100. Answers should berounded to the nearest hundredth. (1)______________________________________

8c) Looking at parts a and b, what happens to the standard error as the sample size increases?___________________________________________________________________________(1)

8d) What is the central limit theorem? __________________________________________________________________________________________________________________________(1)

8e) What is the mean of the distribution?______________________________________ (1)

Please do this problem by hand. Answers given by the calculator function will not get fullcredit.

8f) Determine the probability of selecting a sample of 50 nonresidential buildings that will havea mean age of 30.5 years or less. Answers should be rounded to the nearest thousandth. (2)**Show:

• Formulas

• Pictures

• calculations

• use Table II

-Standard Normal Table.

9) A National Survey conducted by The Social Science Research Center at Old DominionUniversity found that 56% of all drivers admitted they run red lights. Assume this proportion istrue for the population of all US drivers.

9a) What is the population parameter? ___________________________________________(1)

9b) What is p?_______________________ (1)

If a random sample of 500 drivers is selected from this population.

9c) How many drivers in the sample admit to running red lights? ______________________(1)

9d) What is the mean of the sampling distribution of the proportion of drivers that run redlights? Use the correct notation.__________________________(1)

9e) What is the standard error of the sampling distribution of the proportion of drivers that runred lights? Use the correct notation, formula and round to nearest hundredth. (1)________________________

9f) Does this distribution satisfy the Central Limit Theorem? Show why or why not. (1)_____________________________________________________________________________

9g) A National Survey conducted by The Social Science Research Center at Old DominionUniversity found that 56% of all drivers admitted they run red lights. Assume this proportion istrue for the population of all US drivers. If a random sample of 500 drivers is selected from thispopulation, then determine the probability that the sample proportion, ??, of drivers who admitto running red lights is greater than 61%.Using the information, you found in the prior steps of this problem, please find the probabilityabove.

Please do this problem by hand. Answers given by the calculator function will not getfull credit. (2)**Show:

• Formulas

• Pictures

• calculations

• use Table II

-Standard Normal Table.