A company tracks the number of complaints they receive, where the random variable X is the number of complaints received daily. Find the variance & standard deviation of this distribution.

• A. Variance = 0.83; Standard Deviation = 0.9
• B. Variance = 0.9; Standard Deviation = 0.83
• C. Variance = 0.83; Standard Deviation = 0.85
• D. Variance = 0.85; Standard Deviation = 0.9

Answer: (A)

Verified step by step guidance

1. Calculate the expected value (mean) of the distribution using the formula: E(X) = Σ [x * P(x)], where x is the number of complaints and P(x) is the probability of x.
2. Substitute the values from the table into the formula: E(X) = (0 * 0.45) + (1 * 0.30) + (2 * 0.20) + (3 * 0.05).
3. Calculate the variance using the formula: Var(X) = Σ [(x - E(X))^2 * P(x)].
4. Substitute the expected value and the values from the table into the variance formula: Var(X) = [(0 - E(X))^2 * 0.45] + [(1 - E(X))^2 * 0.30] + [(2 - E(X))^2 * 0.20] + [(3 - E(X))^2 * 0.05].
5. Calculate the standard deviation by taking the square root of the variance: SD(X) = √Var(X).