Exploring the Normal Distribution in AP Statistics

What does it mean for a value to be considered extreme in a normal distribution?

• It falls within one standard deviation of the mean.

• It is exactly equal to the mean.

• It has a probability under 1% or 5%.

• It falls within the middle 50% of the distribution.

In the context of a normal distribution, what does a z-score represent?

• The total area under the curve.

• The mean of the distribution.

• The number of standard deviations a value is from the mean.

• The probability of an event occurring.

If Josh takes 23.14 minutes or more to wash a car, what can be said about this time?

• It is considered extremely low.

• It is within the middle 50% of times.

• It is the mean time.

• It is in the top 1% of times.

What is the first step in finding the time that marks an extremely low value for washing a car?

• Determine the z-score for the top 1%.

• Calculate the mean time.

• Decide if the extreme value is in the bottom 1% or 5%.

• Find the standard deviation.

For high school boys' bench press weights, what is the mean weight?

• 200 pounds

• 34.5 pounds

• 140.2 pounds

• 125 pounds

What is the probability that a high school boy can bench press more than 200 pounds?

• 0.2634

• 0.0744

• 0.0415

• 0.3298

What z-score represents the top 1% in a normal distribution?

• 1.1750

• 0.8416

• 2.3263

• -1.6449

If a high school boy's bench press weight is 190 pounds, is this considered significantly high?

• Yes, because it is in the top 1%.

• No, because it is below the mean.

• No, because the probability is about 7%.

• Yes, because it is above the mean.

In the fish length example, what is the standard deviation if 12% of fish are above 25 inches?

• 5.53

• 6.50

• 1.1750

• 18.5

What is the probability that a fish in the lake is below 15 inches?

• 0.0415

• 0.0744

• 0.2634

• 0.3298