Statistics and Normal Distribution Concepts

The video tutorial covers two problems from AP statistics. The first problem involves calculating the z-score for an exam score of 5, given a mean and standard deviation. The tutorial clarifies that z-scores can be used for non-normal distributions. The second problem involves calculating the probability of a fifth-grade boy being taller than 157.7 cm, using the empirical rule for normal distributions.

What is the mean score of the 2007 AP statistics examination mentioned in the video?

• 3.0

• 5.0

• 1.34

• 2.8

How do you calculate the z-score for a given exam score?

• Subtract the mean from the score and divide by the standard deviation

• Add the score to the standard deviation and divide by the mean

• Add the mean to the score and multiply by the standard deviation

• Subtract the standard deviation from the score and divide by the mean

What is the z-score for an exam score of 5?

• 1.34

• 2.8

• 1.64

• 5.0

Can a z-score be calculated for a non-normal distribution?

• No, it is not applicable to any distribution

• Yes, but only if the distribution is skewed

• No, it can only be calculated for normal distributions

• Yes, it can be calculated for any distribution with a mean and standard deviation

What is the mean height of fifth-grade boys in the United States as mentioned in the video?

• 7.1 cm

• 150.6 cm

• 143.5 cm

• 157.7 cm

What is the standard deviation of the height of fifth-grade boys?

• 157.7 cm

• 150.6 cm

• 143.5 cm

• 7.1 cm

What is the probability that a randomly chosen fifth-grade boy is taller than 157.7 cm?

• 68%

• 5%

• 95%

• 2.5%

According to the empirical rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

• 68%

• 95%

• 50%

• 99.7%

What is the empirical rule also known as?

• The 60-90-100 rule

• The 70-80-90 rule

• The 50-75-100 rule

• The 68-95-99.7 rule

What is the area under the normal distribution curve that is more than two standard deviations from the mean?

• 1%

• 2.5%

• 5%

• 10%