Question
b. The mean, median, and mode are equal in a normal diser Is this statement true or false? Explain your answer. c. A normal distribution is bimodal. Is this statement true or false? Explain your answer. d. In a normal distribution, exactly 50% of the population is within one standard deviation of the mean. Is this statement true or false? Explain your answer.
Solution
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Jaliyah
Master ยท Tutor for 5 years
Answer
### b. True. In a normal distribution, the mean, median, and mode are all equal.### c. False. A normal distribution is unimodal, having only one peak at the mean.### d. False. Approximately 68% of the population is within one standard deviation of the mean in a normal distribution.
Explanation
## Step 1: Mean, Median, and Mode in a Normal Distribution### A normal distribution is a symmetrical, bell-shaped distribution where the mean, median, and mode are all equal and located at the center of the distribution. This is a fundamental property of normal distributions.## Step 2: Modality of a Normal Distribution### A normal distribution has only one peak, located at the mean. This means it is unimodal, not bimodal. A bimodal distribution has two distinct peaks.## Step 3: Percentage within One Standard Deviation### In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This is a key characteristic often referred to as the 68-95-99.7 rule (or the empirical rule).