Decide which of the described variables is/are likely to have a normal or near-normal distribution.
a) The heights of corn stalks in one row of corn that is half a mile long
b) The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values)
A. a
B. b
C. a and b
D. neither
Answer: b
I believe it is A
To determine which of the variables is likely to have a normal or near-normal distribution, we need to consider the characteristics of normal distribution.
A normal distribution, also known as a bell curve, is symmetric around the mean. It has a single peak and most of the data falls within a few standard deviations of the mean.
Let's analyze each variable:
a) The heights of corn stalks in one row of corn that is half a mile long:
In this case, the heights of corn stalks are likely to vary, and it is unlikely that they will follow a normal distribution. Factors such as genetics, environmental conditions, and growth patterns can lead to significant variations in the height of corn stalks. Therefore, variable a) is unlikely to have a normal or near-normal distribution.
b) The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values):
In this case, the number of viewers for each channel is expected to have a wider range of values, however, it is possible that it follows a normal or near-normal distribution. It is reasonable to assume that the popularity of TV channels across a large audience may follow a pattern close to normal distribution, with some channels having higher viewership and others having lower viewership. Therefore, variable b) is likely to have a normal or near-normal distribution.
Therefore, the answer is option B - variable b) is likely to have a normal or near-normal distribution.