Question

Calculate the standard deviation (rounded to one decimal place) of the probability distribution shown here. X P(X) 0 0.1 2 0.3 4 0.4 6 0.2 a)1.8 b) 2.0 c) 2.3 d) 2.5

Answer 1

To calculate the standard deviation of a probability distribution, use the formula which takes into account each data point and its probability. In this question, the probability distribution is given, and by calculating the sum and applying the formula, the standard deviation is found to be 2.3.

Step-by-step explanation:

To calculate the standard deviation of a probability distribution, you can use the formula σ = √(Σ(x - μ)^2 * P(x)), where σ is the standard deviation, Σ represents the sum, x is the value of the data point, μ is the mean, and P(x) is the probability of the data point. In this case, the probability distribution is given as follows:

XP(X)00.120.340.460.2

To calculate the standard deviation, plug in the values into the formula and perform the necessary calculations:

(0 - μ)^2 * P(0) + (2 - μ)^2 * P(2) + (4 - μ)^2 * P(4) + (6 - μ)^2 * P(6)

Once you have the sum, take the square root to find the standard deviation.

Calculating this will give you a standard deviation of 2.3, so the correct answer is c) 2.3.