Density Curves AP Stat

The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range

• 65.5 - 70.5 in

• 63 - 73 in

• 60.5 - 75.5 in

• 58 - 78 in

• none of the above

The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. About what percentage of the men are over 70.5 inches tall?

• 2.5

• 5

• 16

• 32

• 68

For this density curve, which statement is true?

• The area under the curve between 0 and 1 is 1

• The density curve is symmetric

• The density curve is skewed right

• The density curve is Normal

• None of the above is correct

The area under the Standard Normal curve corresponding to -0.3 < z < 1.6 is

• .3273

• .4713

• .5631

• .9542

• None of the above

The graph at right is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true?

• The distribution is Normal

• The distribution is Uniform

• The distribution is skewed left

• The distribution is skewed right

• The distribution is Symmetrical

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is

• Normally distributed, with mean 30 and standard deviation 15

• Skewed to the right, with mean 30 and standard deviation 15

• Normally distributed, with mean 0 and standard deviation 1

• Skewed to the right, with mean 0 and standard deviation 1

• Skewed to the right, but need more information to find mean and standard deviation

The cumulative relative frequency graph shows the distribution of lengths (in cm) of fingerlings at a fish hatchery. The interquartile range for this distribution is

approximately:

• 0.18 to 0.85 cm

• 5 to 7 cm

• 5.5 to 6.7 cm

• 1.2 cm

• 2 cm

Which of the following properties is true for all Normal density curves?

I. They are symmetric.

II. The curve reaches its peak at the mean.

III. 95% percent of the area under the curve is within one standard deviation of the mean.

• I only

• II only

• I and II only

• I and III only

• All three statements are correct

A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what proportion of their response times is over 30 minutes?

• .03

• .21

• .25

• .75

• .79

A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. In how about many minutes is their response time in their fastest 10% responses?

• 2.2 minutes

• 6.8 minutes

• 22 minutes

• 23.2 minutes

• 37.2 minutes