Normal Distribution Table Review:

1. Two standard deviations away from the mean contains ABOUT 95% of the population.  This estimate is useful in constructing confidence intervals.  Sketch a normal distribution.  Shade in the middle 95%.

 a. What percent of the curve is in each tail?____________
 b. Use the your results from (a) and the normal probability table in the front of the text to find how many standard deviations each tail is from the mean.  (It's symmetric, so you only need to look up one of the tails.)
 c. We have been using 2 standard deviations to approximate  a 95% confidence interval.  How far off were we?

2. Using the normal probability table, we can construct confidence intervals of any size...70%, 90%, 99%, and so on.
 a. Of the three sizes suggested above, which confidence interval would be the largest?__________
 b. What proportion of the normal distribution would be in each tail for a
                  70% confidence interval: _______ in each tail
                  90% confidence interval: _______ in each tail
                  99% confidence interval: _______ in each tail
 c. Look up the values obtained from part (b) on the normal probability table, and find how many standard deviations would be needed on each side of the mean to construct the confidence interval.
                  70% confidence interval = _______ standard deviations
                  90% confidence interval = _______ standard deviations
                  99% confidence interval = _______ standard deviations

3. Lucky for you, there is a convenient table which provides the required number of standard deviations for a variety of confidence intervals.  Look on p. T-11 in the back of your text (blue edged pages).  Look at the very bottom of the table where it says "Confidence level C".  Just above that are different sizes of confidence intervals, given as percents.  The final entry of the table values (on the infinity row) are the standard deviations.
 a. Check your values in 2(c) to make sure you are correct.
 b. Suppose you want to construct an 80% confidence interval, how many standard deviations would you include on each side of the mean?_________

4. When 500 high school students are randomly selected and surveyed, it is found that 135 have been kidnaped by aliens.  Find a 98% confidence interval for the true proportion of all high school students who have been kidnaped by aliens.
 

5. In doing market research for the "Beanie Hat With the Twirly Thing On Top" company, you find that a random sample of 1220 math nerds include 1054 which own a beanie hat with a twirly thing on top.  Based on those results, construct a 90% confidence interval for the proportion of math nerds  which own such a hat.
 

6. In a SRS of 100 LHS students, you find that 65% belong to CAA (Cute and Available).  Construct a 99.9% confidence interval for the proportion of LHS students that are CAA.