11.2 Review questions

Find the 95% confidence interval for the true proportion of U.S. girls, age 12 - 19, who have been pregnant.

The report also stated that the results of the survey are accurate to within ± 3.7% at the 95% confidence level. Suppose that a new study is to be done. It is desired to be accurate to within 2% of the 95% confidence level. What will happen to the minimum number that should be surveyed?

Given: $X$ ~ $\text{Exp}\left(\frac{1}{3}\right)$ . Sketch the graph that depicts: $P\left(X>1\right)$ .

60% of individuals keep their cars at most how many years?

Suppose that we randomly survey one person. Find the probability that person keeps his/her car less than 2.5 years.

If we are to pick individuals 10 at a time, find the distribution for the average car length ownership.

If we are to pick 10 individuals, find the probability that the sum of their ownership time is more than 55 years.

For which distribution is the median not equal to the mean?

• A

  Uniform

• B

  Exponential

• C

  Normal

• D

  Student-t

Compare the standard normal distribution to the student-t distribution, centered at 0. Explain which of the following are true and which are false.

• A

  As the number surveyed increases, the area to the left of -1 for the student-t distribution approaches the area for the standard normal distribution.

• B

  As the number surveyed increases, the area to the left of -1 for the standard normal distribution approaches the area for the student-t distribution.

• C

  As the degrees of freedom decrease, the graph of the student-t distribution looks more like the graph of the standard normal distribution.

• D

  If the number surveyed is less than 30, the normal distribution should never be used.