Consider the given probability distribution. What is the standard deviation? Express your answer into 2 decimal places (example: 25.00)
(x, 0, 1, 2, 3, 4, 5)
(p (x) 0.003, 0.045 0.34, 0.54, 0.55, 0.262)
Share
Consider the given probability distribution. What is the standard deviation? Express your answer into 2 decimal places (example: 25.00)
(x, 0, 1, 2, 3, 4, 5)
(p (x) 0.003, 0.045 0.34, 0.54, 0.55, 0.262)
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
To find the standard deviation of a probability distribution, we need to calculate the variance first. The variance is given by the formula:
Var(X) = Σ [ (x - μ)^2 * p(x) ]
where Σ denotes the sum, x represents the values, μ is the mean, and p(x) is the probability of each value.
Let's calculate the variance step by step:
Step 1: Calculate the mean (μ)
μ = Σ (x * p(x))
= (0 * 0.003) + (1 * 0.045) + (2 * 0.34) + (3 * 0.54) + (4 * 0.55) + (5 * 0.262)
= 0 + 0.045 + 0.68 + 1.62 + 2.2 + 1.31
= 5.925
Step 2: Calculate the squared differences from the mean [(x - μ)^2]
Squared Difference for x = 0: (0 - 5.925)^2 * 0.003
Squared Difference for x = 1: (1 - 5.925)^2 * 0.045
Squared Difference for x = 2: (2 - 5.925)^2 * 0.34
Squared Difference for x = 3: (3 - 5.925)^2 * 0.54
Squared Difference for x = 4: (4 - 5.925)^2 * 0.55
Squared Difference for x = 5: (5 - 5.925)^2 * 0.262
Step 3: Calculate the variance (Var(X))
Var(X) = Σ [ (x - μ)^2 * p(x) ]
= [(0 - 5.925)^2 * 0.003] + [(1 - 5.925)^2 * 0.045] + [(2 - 5.925)^2 * 0.34] + [(3 - 5.925)^2 * 0.54] + [(4 - 5.925)^2 * 0.55] + [(5 - 5.925)^2 * 0.262]
= 35.273725
Step 4: Calculate the standard deviation (σ)
σ = √Var(X)
= √35.273725
= 5.94 (rounded to 2 decimal places)
Therefore, the standard deviation of the given probability distribution is 5.94.