Answer:
To calculate the mean and standard deviation for the given data:
Calculate the weighted sum of the products of each number and its corresponding probability:
(2 * 0.2) + (6 * 0.1) + (8 * 0.25) + (11 * 0.45)
The result is the mean of the data set.
To calculate the standard deviation, you can use the formula:
sqrt[((2-mean)^2 * 0.2) + ((6-mean)^2 * 0.1) + ((8-mean)^2 * 0.25) + ((11-mean)^2 * 0.45)]
The square root of this value will give you the standard deviation of the data set.
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