Question

question 17 which one of the following statements is true? if a distribution is symmetric, it must be a normal distribution. in a normal distribution, 95% of the data values will fall within one standard deviation of the mean. in a normal distribution, the mean is equal to the median. a z - score can never be negative. the mean and standard deviation are included in the five - number summary.

Explanation:

• A symmetric distribution can be other types, not just normal, so the first statement is false.
• In a normal distribution, about 68% of data falls within one - standard deviation of the mean, not 95%, so the second statement is false.
• A normal distribution is symmetric, and for symmetric distributions, the mean equals the median, so the third statement is true.
• A z - score can be negative when a data point is below the mean, so the fourth statement is false.
• The five - number summary consists of the minimum, first quartile, median, third quartile, and maximum, not the mean and standard deviation, so the fifth statement is false.

Answer:

In a Normal distribution, the mean is equal to the median.