Question

One normal distribution has a mean of 5 and a standard deviation of 2. A second normal distribution has a mean of 6 and a standard deviation of 1. Which of the following statements is true?

Select one:

a. The dispersions of both distributions are the same.

b. The width of the first distribution is wider than the second distribution.

c. The central location of the first distribution is higher than the second distribution.

d. The locations of both distributions are the same.

Answer 1

One normal distribution has mean 5 and standard deviation of 2.

A second normal distribution has a mean of 6 and standard deviation of 1.

Now, the mean is actually the location of the distribution, standard deviation is actually the width.

Now, the dispersions are not the same, because the standard deviations are different. So, the first statement is false.

The locations of them are also not same, because the means are different. So, the last statement is false.

Now, the central location of the first distribution is 5, that for the second one is 6. So, the third statement is false.

Now, the width of the first distribution is 2, that for the second one is 1; so the first distribution is wider.

So, the correct answer is option (b) The width of the first distribution is wider than the second distribution.