Question

True or​ false: the mean of a normal distribution has no effect on its spread. explain your answer. choose the correct answer below.
a. false. the spread of a normal distribution is completely determined by its mean.
b. true. the spread of a normal distribution is completely determined by its standard deviation.
c. true. the spread of a normal distribution is completely determined by its median.
d. false. the spread of a normal distribution is determined by both its mean and standard deviation.

Answer 1

b. true. the spread of a normal distribution is completely determined by its standard deviation. A normal distribution is defined by 2 values, its mean and it's standard distribution. The standard distribution determines what the shape of the curve looks like. A small distribution causes the curve to be tall and skinny. A large distribution causes the curve to be short and fat. The overall shape is entirely determine by the standard deviation. The exact location of the peak is determined by the mean. So let's look at the options and see why they're right or wrong. a. false. the spread of a normal distribution is completely determined by its mean. * This is exactly wrong. The mean determines where the peak is, the shape is determined by the standard distribution. b. true. the spread of a normal distribution is completely determined by its standard deviation. * This is absolutely correct. c. true. the spread of a normal distribution is completely determined by its median. * Once again, it's swapping the meaning between mean and standard distribution. d. false. the spread of a normal distribution is determined by both its mean and standard deviation. * This is a bit of weasel wording here. But remember, the SHAPE is determined by the standard distribution while the location of the peak is determined by the mean.