Of the following variables, which would NOT exhibit normal distributions?
I: Height, Weight
II: Test Scores
III: Flipping a coin
Select one:
a. I Only
b. III Only
c. I and II
d. I, II, and III
which ones have a continuous range, rather than discrete?
To determine which of the variables would NOT exhibit normal distributions, we need to understand what a normal distribution is and consider the characteristics of each variable.
A normal distribution, also known as a bell curve, is a symmetrical probability distribution where the majority of values cluster around the mean, and fewer values are found in the tails. In a normal distribution, the mean, median, and mode are all equal.
Now let's analyze each variable:
I: Height, Weight:
Both height and weight can be expected to exhibit normal distributions in a given population because they are influenced by multiple factors and have a large number of possible values. Therefore, variable I is likely to exhibit a normal distribution.
II: Test Scores:
Test scores can vary based on the difficulty of the test and the performance of the individuals taking it. However, test scores are often influenced by factors such as knowledge, preparation, and effort. Therefore, test scores are less likely to exhibit a normal distribution. Other distributions, such as skewed or bimodal distributions, are possible for test scores depending on the factors affecting them.
III: Flipping a coin:
Flipping a coin is a random process where there are two possible outcomes (heads or tails) with an equal probability. The resulting distribution of flipping a fair coin many times is a binomial distribution, not a normal distribution. In a binomial distribution, the outcomes are discrete (i.e., whole numbers) rather than continuous like in a normal distribution.
Based on the explanations above, the variable that would NOT exhibit a normal distribution is:
b. III Only (Flipping a coin)
Therefore, the correct answer is b.