Understanding Normal Distributions
Math · Learn by Concept
Help Questions
Math › Understanding Normal Distributions
If a population has a normal distribution, the number of values within one positive standard deviation of the mean will be . . .
equal to the number of values within one negative standard deviation of the mean
fewer than the number of values within one negative standard deviation of the mean
at least 40% of all values in the population
fewer than 20% of all values in the population
equal to the number of values within two negative standard deviations of the mean
Explanation
In a normal distribution, the number of values within one positive standard deviation of the mean is equal to the number of values within one negative standard deviation of the mean. The reason for this is that the values below the population mean exactly parallel the values above the mean.
Which of the following populations has a precisely normal distribution?
Explanation
A normal distribution is one in which the values are evenly distributed both above and below the mean. A population has a precisely normal distribution if the mean, mode, and median are all equal. For the population of 3,4,5,5,5,6,7, the mean, mode, and median are all 5.