Recall the Empirical Rule from Chapter 3. It states that if the data distribution is bell shaped, then the interval contains approximately

Recall the Empirical Rule from Chapter 3. It states that if the data distribution is bell shaped, then the interval μ ± σ contains approximately 68% of the values, μ ± 2 s contains approximately 95%, and μ ± 3 s contains virtually all of the data values.
The bell-shaped distribution referenced is the normal distribution.
a. Verify that a standard normal distribution contains approximately 68% of the values in the interval μ ± σ.
b. Verify that a standard normal distribution contains approximately 95% of the values in the interval μ ± 2σ.
c. Verify that a standard normal distribution contains virtually all of the data in the interval μ ± 3σ.