Multiple Choice
Given the data set: , , , , what is the mean of the data?
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3. Describing Data Numerically
Mean
Multiple Choice
Which of the following formulas is the easiest way to calculate the mean of a binomial distribution?
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Verified step by step guidance1
Recall that a binomial distribution models the number of successes in \( n \) independent trials, each with success probability \( p \).
The mean (or expected value) of a binomial distribution is given by the formula \( \mu = n \times p \).
This formula represents the average number of successes you would expect over \( n \) trials.
Other formulas given, such as \( n + p \), \( \frac{n}{p} \), or \( \sqrt{n \times p \times (1 - p)} \), correspond to different statistics (e.g., variance or standard deviation) or are incorrect for the mean.
Therefore, the easiest and correct way to calculate the mean of a binomial distribution is to multiply the number of trials \( n \) by the probability of success \( p \), i.e., \( \mu = n \times p \).
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