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
To decide which of the described variables is likely to have a normal or near-normal distribution, we need to consider the characteristics of a normal distribution. A normal distribution, also known as a bell curve, is symmetrical and has most of its values concentrated around the mean, with fewer values in the tails.
a) The heights of corn stalks in one row of corn that is half a mile long:
It is unlikely that the heights of corn stalks will follow a normal distribution. Corn stalk heights may vary due to factors such as genetic variation, growing conditions, and other environmental factors. As a result, the distribution of corn stalk heights may not be symmetric or follow a recognizable pattern.
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):
The number of viewers of each channel on Direct TV is more likely to have a normal or near-normal distribution. When there are a large number of random events or variables contributing to the overall count (in this case, the number of viewers for each channel), it tends to result in a distribution that approximates a normal distribution. Additionally, if we have a sufficiently large sample size (349 data values in this case), it becomes more likely that the distribution will approximate a normal distribution.
Therefore, the answer is 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).
To determine whether the described variables are likely to have a normal or near-normal distribution, we can consider the characteristics of each variable.
a) The heights of corn stalks in one row of corn that is half a mile long:
The heights of corn stalks are typically influenced by several factors, such as genetics, soil quality, and weather conditions. These factors can lead to natural variations in height, which could result in a distribution that approximates a normal distribution. Thus, variable a) is likely 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:
The number of viewers for each channel is not influenced by natural factors that tend to lead to normal distributions. Instead, the number of viewers for specific TV channels can be affected by factors such as popularity, program content, and audience preferences. These factors are subjective and can lead to distributions that deviate from a normal distribution. Therefore, variable b) is not likely to have a normal or near-normal distribution.
Based on these considerations, the correct answer is D. Neither a) nor b) is likely to have a normal or near-normal distribution.