Based on the below table, answer the following question:xP(x)30.0540.4050.3060.1570.10What is the standard deviation?Question 3Answera.4.85b.1.06c.0.3

To calculate the standard deviation, we first need to calculate the expected value (mean), then the variance, and finally take the square root of the variance to get the standard deviation.

1. Calculate the expected value (mean): E(X) = Σ [x * P(x)] E(X) = (30.05) + (40.4) + (50.3) + (60.15) + (7*0.1) = 0.15 + 1.6 + 1.5 + 0.9 + 0.7 = 4.85

2. Calculate the variance: Var(X) = Σ [(x - E(X))^2 * P(x)] Var(X) = [(3-4.85)^2 * 0.05] + [(4-4.85)^2 * 0.4] + [(5-4.85)^2 * 0.3] + [(6-4.85)^2 * 0.15] + [(7-4.85)^2 * 0.1] Var(X) = 0.17625 + 0.34 + 0.0225 + 0.17325 + 0.4635 = 1.1755

3. Calculate the standard deviation: SD(X) = sqrt(Var(X)) = sqrt(1.1755) = 1.0842

So, the standard deviation is approximately 1.08, which is not exactly any of the options given. There might be a mistake in the question or the options provided.

To calculate the standard deviation, we first need to calculate the expected value (mean), then the variance, and finally take the square root of the variance to get the standard deviation.

1. Calculate the expected value (mean): Multiply each value of x by its probability and sum them up. E(x) = Σ [x * P(x)] = (30.05) + (40.4) + (50.3) + (60.15) + (7*0.1) = 0.15 + 1.6 + 1.5 + 0.9 + 0.7 = 4.85

2. Calculate the variance: Subtract the mean from each x, square the result, multiply by the probability, and sum them up. Var(x) = Σ {[(x - μ)^2] * P(x)} = [(3-4.85)^2 * 0.05] + [(4-4.85)^2 * 0.4] + [(5-4.85)^2 * 0.3] + [(6-4.85)^2 * 0.15] + [(7-4.85)^2 * 0.1] = 0.067025 + 0.2898 + 0.00675 + 0.1663125 + 0.231525 = 0.7614125

3. Calculate the standard deviation: The standard deviation is the square root of the variance. σ = √Var(x) = √0.7614125 = 0.8723 (approximately)

So, the standard deviation is not listed in the provided options (a.4.85, b.1.06, c.0.3). There might be a mistake in the question or the options provided.