Which statement about the standard normal distribution is true?

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Multiple Choice

Which statement about the standard normal distribution is true?

The standard normal distribution is a normal distribution with mean 0 and standard deviation 1, and about 68% of its probability lies within one standard deviation of the mean. Since that corresponds to z values from -1 to 1, the area under the curve between z = -1 and z = 1 is about 68%. That makes the statement true. The other ideas aren’t correct: a normal distribution’s mean isn’t always zero—only the standard normal has mean 0. The standard deviation isn’t constrained to be larger than the mean; it can be greater or smaller depending on the distribution. And the 95% area is within two standard deviations, not one.

The standard normal distribution is a normal distribution with mean 0 and standard deviation 1, and about 68% of its probability lies within one standard deviation of the mean. Since that corresponds to z values from -1 to 1, the area under the curve between z = -1 and z = 1 is about 68%. That makes the statement true.

The other ideas aren’t correct: a normal distribution’s mean isn’t always zero—only the standard normal has mean 0. The standard deviation isn’t constrained to be larger than the mean; it can be greater or smaller depending on the distribution. And the 95% area is within two standard deviations, not one.

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