The following probability distribution represents the number of grievances filed per month with the MNM. Corporation.x f(x)0 0.041 0.362 0.503 0.084      0.02a. Compute the standard deviation.Question 10Select one:a.4.5b.2.66c.1.5d.3.66

To compute the standard deviation of a probability distribution, we first need to calculate the expected value (mean), and then use this to find the variance. The standard deviation is the square root of the variance.

Here are the steps:

1. Calculate the expected value (mean): Multiply each possible outcome by its probability and sum these values. This gives us the expected value E(x).

E(x) = Σ [x * P(x)] = (00.04) + (10.36) + (20.50) + (30.08) + (4*0.02) = 0 + 0.36 + 1.00 + 0.24 + 0.08 = 1.68

2. Calculate the variance: Subtract the expected value from each possible outcome, square the result, and multiply by the probability of the outcome. Sum these values to get the variance Var(x).

Var(x) = Σ [(x - E(x))^2 * P(x)] = [(0 - 1.68)^2 * 0.04] + [(1 - 1.68)^2 * 0.36] + [(2 - 1.68)^2 * 0.50] + [(3 - 1.68)^2 * 0.08] + [(4 - 1.68)^2 * 0.02] = [2.8224 * 0.04] + [0.4624 * 0.36] + [0.1024 * 0.50] + [1.7664 * 0.08] + [5.4224 * 0.02] = 0.112896 + 0.166464 + 0.0512 + 0.141312 + 0.108448 = 0.58032

3. Calculate the standard deviation: This is the square root of the variance.

Standard Deviation =

To compute the standard deviation of a probability distribution, we first need to calculate the expected value (mean), and then use this to find the variance. After finding the variance, the standard deviation is the square root of the variance.

Here are the steps:

1. Calculate the expected value (mean): Multiply each possible outcome by its probability and then sum these values.

   E(x) = Σ [x * P(x)] = (0 * 0.04) + (1 * 0.36) + (2 * 0.50) + (3 * 0.08) + (4 * 0.02) = 0 + 0.36 + 1.00 + 0.24 + 0.08 = 1.68

2. Calculate the variance: Subtract the expected value from each possible outcome, square the result, and multiply by the probability of the outcome. Then sum these values.

   Var(x) = Σ { [x - E(x)]² * P(x) } = [ (0 - 1.68)² * 0.04 ] + [ (1 - 1.68)² * 0.36 ] + [ (2 - 1.68)² * 0.50 ] + [ (3 - 1.68)² * 0.08 ] + [ (4 - 1.68)² * 0.02 ] = 0.112896 + 0.166464 + 0.0512 + 0.14112 + 0.027072 = 0.498752

3. Calculate the standard deviation: This is the square root of the variance.

   SD = √Var(x) = √0.498752 = 0.7062 (approximately)

So, the standard deviation is approximately 0.7062. However, this option is not available in your list. Please check the problem or the options again.