Statistics

For any binomial distribution, the mean is calculated using the formula E(X) = np, where n is the number of trials and p is the probability of success, yielding 10 * 0.4 = 4. Distractors like C represent the midpoint of the trials, which is only the mean when the probability of success is exactly 0.5.

The expected value E(X) is calculated by summing the products of each outcome and its probability, giving (1 * 0.3) + (2 * 0.5) + (3 * 0.2) = 1.9. Option A is incorrect because 1.5 is simply the midpoint of the outcomes, which fails to account for the actual probability distribution of the variable.

The expected value E(X) is calculated by summing the products of each outcome and its probability, giving (1 * 0.3) + (2 * 0.5) + (3 * 0.2) = 1.9. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option A is incorrect because 1.5 is simply the midpoint of the outcomes, which fails to account for the actual probability distribution of the variable.
• !Option A is incorrect because the mean alone only gives the location of the peak but cannot describe how wide or narrow the curve is.
• !Option B is incorrect because a Type II error occurs when we fail to reject a null hypothesis that is actually false, representing a false negative.

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