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?Number of OscarsP(x)10.5620.2330.1140.0550.0360.02 1 point1.821.1961.32
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?Number of OscarsP(x)10.5620.2330.1140.0550.0360.02 1 point1.821.1961.32
Solution
To calculate the standard deviation of a probability distribution, we first need to calculate the expected value (mean), and then use this to calculate the variance, the square root of which is the standard deviation.
The expected value (E) is calculated as follows:
E = ∑ [x * P(x)] = (10.56) + (20.23) + (30.11) + (40.05) + (50.03) + (60.02) = 0.56 + 0.46 + 0.33 + 0.20 + 0.15 + 0.12 = 1.82
The variance is calculated as follows:
Var = ∑ [(x - E)^2 * P(x)] = [(1 - 1.82)^2 * 0.56] + [(2 - 1.82)^2 * 0.23] + [(3 - 1.82)^2 * 0.11] + [(4 - 1.82)^2 * 0.05] + [(5 - 1.82)^2 * 0.03] + [(6 - 1.82)^2 * 0.02] = 0.18 + 0.01 + 0.02 + 0.02 + 0.03 + 0.03 = 0.29
The standard deviation is the square root of the variance:
SD = √Var = √0.29 = 0.54
So, the standard deviation of this distribution is approximately 0.54. However, this option is not provided in the choices. There might be a mistake in the question or the provided options.
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