Question

1. for the density curve shown, which statement is true?

a. the mean is greater than the median.
b. the mean is less than the median.
c. the mean and median are equal.
d. the mean could be either greater than or less than the median.
e. none of the above is correct.

1. you can roughly locate the mean of a density curve by eye because it is

a. the point at which the curve would balance if made of solid material.
b. the point that divides the area under the curve into two equal parts.
c. the point at which the curve reaches its peak.
d. the point where the curvature changes direction.
e. the point at which the height of the graph is equal to 1.

1. the graph below is a normal probability plot for the amount of rainfall (in acre - feet) obtained from 26 randomly selected clouds that were seeded with silver oxide.

which of the following statements about the shape of the rainfall distribution is true?
a. the distribution is normal.
b. the distribution is approximately normal.
c. the distribution is skewed to the left.
d. the distribution has no potential outliers.
e. the distribution is skewed to the right.

Explanation:

Question 8

The density curve is symmetric (mirror image on both sides of its peak). For symmetric density curves, the mean and median are equal, as they both lie at the center of symmetry.

Question 9

The mean of a density curve represents the "balance point" of the curve (if it were a solid object, this is where it would balance). The median splits the area under the curve in half, the peak is the mode, and curvature change points are inflection points.

Question 10

A normal probability plot with points curving upward (concave up) indicates the underlying distribution is right-skewed. This shape occurs because the upper tail of the distribution is longer, pulling the upper points away from a straight line.

Answer:

1. c. The mean and median are equal.
2. a. the point at which the curve would balance if made of solid material.
3. e. The distribution is skewed to the right.