Density Curves AP Stat

For the density curve shown, which of the following statements is true?

• The mean is larger than the median.

• The proportion of outcomes between 0.2 and 0.5 is equal to 0.3.

• The total area under the curve is greater than 1.

• The proportion of outcomes greater than 1.5 is equal to 0.25.

An office uses two brands of fluorescent light bulbs in its overhead light fixtures. From past experience, it is known that Brand A bulbs have a mean life length of 3000 hours and a standard deviation of 200 hours, while Brand B bulbs have a mean life length of 2700 hours and a standard deviation of 250 hours. Which bulb has a longer life relative to all bulbs of its brand, a Brand A bulb that lasts 3150 hours or a Brand B bulb that lasts 2850 hours?

• The Brand A bulb has a longer life relative to its brand.

• The Brand B bulb has a longer life relative to its brand.

• The Brand A bulb has a longer life relative to its brand.

The weights of cockroaches living in a university dormitory follow a Normal distribution with mean 80 grams and standard deviation 5 grams. The percentage of cockroaches having weights between 72 grams and 88 grams must be

• less than 68%.

• between 68% and 95%.

• between 95% and 99.7%.

• between 99.7% and 100%.

Scores on the American College Testing (ACT) college entrance exam follow a Normal distribution with mean 18 and standard deviation 6. Lisa’s standardized score on the ACT was z = -0.7. What was her actual ACT score?

• 4.2

• 13.8

• 17.3

• 22.2

What is the 25th percentile of the standard Normal distribution?

• 1.00

• 0.5987

• -0.6745

• -2.807

The lifetime of a 2-volt battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes that exceed 520 hours is approximately

• 0.2000.

• 0.5793.

• 0.4207.

The lifetime of a 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following is the approximate lifetime of a battery that lasts longer than 90% of all batteries?

• 541.6 hours

• 517.28 hours

• 490.4 hours

The lifetime of 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following best describes the distribution of standard scores for the lifetimes of such batteries?

• Exactly Normal, with mean 0 and standard deviation 1.

• Approximately Normal, with mean 0 and standard deviation 1.

• Approximately Normal, with mean 1 and standard deviation 1.

The graph below is a Normal probability plot of test scores for students in Mr. Olivier’s precalculus classes. Based on this plot, which of the following is the best conclusion about the distribution of test scores?

• Since the Normal probability plot is curved the distribution of test scores is approximately Normal.

• Since the Normal probability plot is curved the distribution of test scores is not approximately Normal.

After accelerating for 20 seconds, a DeLorean sports car has a wide range of speeds that it can achieve, depending on traction. The distribution of speed follows an approximately Normal distribution with a mean of 80 mph and standard deviation of 7.7 mph. Marty wants the next acceleration run to be in the fastest 15% of all possible speeds. How fast will the car have to go?

• 72 mph

• 81 mph

• 86 mph

• 88 mph