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Ana is a dedicated Skee Ball player who always rolls for the 50 point slot. The probability distribution of Ann's score X on a randomly scloctod roll of the ball is shown here. Note that pex = 23.8.

Compare the mean and the median. Basad upon the relationship between the mean and the modian, what is the shape of the probability distribution?

A) The probability distribution is skewed to the right. This relationship makes sense bocause the mean of X is less than the median of X.

B) The probability distribution is skewed to the right. This relationship makes sense because the mean of X is greater than the modian of X.

C) The probability distribution is skewed to the left. This relationship makes sense because the mean of Y is less than the median of X.

D) The probability distribution is symctric. This relationship makes sense because the mean of X is greater than the median of X.

E) The probability distribution is skewed to the Icft. This relationship makes sense because the mean of Y is greater than the median of X.

Ana is a dedicated Skee Ball player who always rolls for the 50 point slot. The probability-example-1
User Ceetheman
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1 Answer

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The probability distribution is skewed to the right since the mean is greater than the median, this indicates a right skew in the probability distribution.

To compare the mean and median and understand the shape of a probability distribution, we need to first recall that if a distribution is skewed to the right (positive skew), the mean is typically greater than the median. Conversely, if a distribution is skewed to the left (negative skew), the mean is typically less than the median. A symmetric distribution has a mean and a median that are close or the same. Without the actual probability distribution values, we rely on the given relationship between the mean and median. Since the question mentions pex = 23.8, we can assume it refers to the mean, though the notation is not standard.

In this case, the correct answer will be the one where the mean is either greater than or less than the median, depending on the skewness described. Answer B represents the correct relationship for a right-skewed distribution: the mean is greater than the median. Therefore, we can infer that the shape of the probability distribution is skewed to the right.

User Metis
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