Question

A museum curator counted the number of paintings in each exhibit at the art museum. Number of paintings Number of exhibits 9 2 21 1 40 1 1 46 3 52 1 67 2 X is the number of paintings that a randomly chosen exhibit has. What is the expected value of x Write your answer as a decimal.

Answer 1

Expected number of paintings that a randomly chosen exhibit has = 40.3

Step-by-step explanation

The expected value of any distribution is calculated as the mean of that distribution.

The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.

Mean = (Σx)/N

x = each variable

Σx = Sum of the variables

N = number of variables

Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)

Σx = 18 + 21 + 40 + 138 + 52 + 134

Σx = 403

N = 2 + 1 + 1 + 3 + 1 + 2 = 10

Mean = (Σx)/N

Mean = (403/10) = 40.3

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