Question

dwayne and alisha both correctly graphed a standard normal curve. which of the following statements is true?

• neither the means nor the standard deviations of dwayne’s and alisha’s graphs must be the same.
• the means of dwayne’s and alisha’s graphs must be the same but not the standard deviations.
• the standard deviations of dwayne’s and alisha’s graphs must be the same but not the means.
• both the means and the standard deviations of dwayne’s and alisha’s graphs must be the same.

Explanation:

A standard normal curve has a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1. By definition, any standard normal curve must have these specific values for mean and standard deviation. So if both Dwayne and Alisha correctly graphed a standard normal curve, their graphs must have the same mean (0) and same standard deviation (1).

Answer:

D. Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.