Question

Consider the normal distribution curve. Which statements are true about the curve? Check all that apply.

a) The standard deviation of the data is 64.

b) The variance of the data is 49.

c) The median is 64.

d) The data point 50 is two standard deviations away from the mean.

Answer 1

Without detailed information about the mean and standard deviation, the given statements about the normal distribution curve cannot be definitively verified.

Step-by-step explanation:

When considering the properties of a normal distribution curve, we can evaluate the given statements.

• The standard deviation (not specified) cannot be determined to be true or false without more context.
• Since variance is the square of the standard deviation, statement 'b' suggests the standard deviation would be the square root of 49, which is 7. This cannot be verified as true or false without more information.
• The median of a normal distribution is equal to the mean, so if the mean is not given as 64, we cannot confirm statement 'c' to be true.
• To determine statement 'd', we would need the mean and the standard deviation of the distribution. 50 is two standard deviations from the mean only if the standard deviation is 7 and the mean is 64.

In summary, without specific details regarding the mean and standard deviation of the data, we cannot definitively validate the statements provided. However, we can state that in any normal distribution, the mean, median, and mode are all located at the same point on the curve.