Probability Density Curves

Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne’s standardized score on the ACT was −0.5. What was Wayne’s actual ACT score?

• 5.5

• 12

• 15

• 17.5

• 21

Two measures of center are marked on the density curve shown. Which of the following is correct?

• The median is at the yellow line and the mean is at the red line.

• The median is at the red line and the mean is at the yellow line.

• The mode is at the red line and the median is at the yellow line.

• The mode is at the yellow line and the median is at the red line.

• .

  The mode is at the red line and the mean is at the yellow line.

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: Point C on this Normal curve corresponds to

• 84 grams.

• 82 grams.

• 78 grams.

• 76 grams.

• 74 grams.

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: About what percent of the cockroaches have weights between 76 and 84 grams?

• 99.7%

• 95%

• 68%

• 47.5%

• 34%

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: About what proportion of the cockroaches will have weights greater than 83 grams?

• 0.0228

• 0.1587

• 0.0772

• 0.9332

• 0.0668

A different species of cockroach has weights that follow a Normal distribution with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. Based on this report, what is the approximate standard deviation of weights for this species of cockroaches?

• 4.6

• .5.0

• 6.2

• 14.0

• Cannot determine without more information

The following Normal probability plot shows the distribution of points scored for the 551 players in the 2011–2012 NBA season.

Question:If the distribution of points was displayed in a histogram, what would be the best description of the histogram’s shape?

• Approximately Normal

• Symmetric but not approximately Normal

• Skewed left

• Skewed right

• Cannot be determined

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 inches to 70.5 inches

• 63 inches to 73 inches

• 60.5 inches to 75.5 inches

• 58 inches to 78 inches

• 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

• 64

For the density curve shown to the right,

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.