Normal Distribution

Concepts

AP Style Example Questions

1. What is the probability of a randomly selected individual having a height within one standard deviation of the mean?

2. How do you calculate the z-score for a given data point in a normal distribution?

3. What is the relationship between the mean, median, and mode in a normal distribution?

Answers to the Example Questions

1. Approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

2. The z-score can be calculated by subtracting the mean from the data point and dividing the result by the standard deviation.

3. In a normal distribution, the mean, median, and mode are all equal.

AP Style Exercises

1. Calculate the z-score for a data point of 75 in a normal distribution with a mean of 60 and a standard deviation of 10.

2. Determine the area under the curve between z = -1 and z = 1 in a standard normal distribution.

3. Find the data point that corresponds to a z-score of -2 in a normal distribution with a mean of 50 and a standard deviation of 5.

Answers to the Exercises

1. The z-score for a data point of 75 is (75 - 60) / 10 = 1.5.

2. The area under the curve between z = -1 and z = 1 in a standard normal distribution is approximately 68%.

3. The data point that corresponds to a z-score of -2 is -2 * 5 + 50 = 40.