Question

The largest number of Oscars received by a film in year X was 4. This was different in previous years. Below is a probability distribution for the number of Oscars per Oscar winning film. What is the standard deviation of this distribution

Answer 1

The standard deviation of the given discrete distribution, considering it's formula, is of 1.195.

How to find the mean and the standard deviation of a discrete distribution?

• The mean is given by the sum of the multiplications of each outcome by it's probability.

• The standard deviation is given by the square root of the sum of the squares of each outcome subtracted by the mean, multiplied by it's probability.

Researching this problem on the internet, the distribution is given by:

• P(X = 1) = 0.56.

• P(X = 2) = 0.23.

• P(X = 3) = 0.11.

• P(X = 4) = 0.05.

• P(X = 5) = 0.03.

• P(X = 6) = 0.02.

Hence the mean is given by:

E(X) = 0.56(1) + 0.23(2) + 0.11(3) + 0.05(4) + 0.03(5) + 0.02(6) = 1.82.

The standard deviation is:

$\sqrt{V(X)} = \sqrt{0.56(1-1.82)^2+0.23(2-1.82)^2+0.11(3-1.82)^2 + \cdots + 0.02(6-1.82)^2} = 1.195$.

More can be learned about the standard deviation of a discrete distribution at https://brainly.com/question/13008984

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