Question

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places I provided a photo image

Answer 1

Answer:
`Standard\text{ devaition = 1.29}`

Step-by-step explanation:

We have been given the probability distribution table where we have x and the probability of x

To find the standard deviation, we need to know the mean. As a result, we will first find the mean of the distribution

`Mean\text{ = }\sum_{i\mathop{=}1}^nx_iP(x_i)`
`\begin{gathered} Mean\text{ = 0 }*0.3\text{ + 1 }*\text{ 0.05 + 2 }*\text{ 0.2 + 2 + 3 }*0.45 \\ Mean\text{ = 1.8} \end{gathered}`
`\begin{gathered} The\text{ formula for standard deviation of a distribution:} \\ Standard\text{ deviation = }\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x}\text{\rparen}^2\text{ }* P(x_i)} \end{gathered}`

`\begin{gathered} From\text{ our computation in the table, }\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2* P(x_i)\text{ = 1.66} \\ Standard\text{ deviation = }\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x}\text{\rparen}^2\text{ }* P(x_i)} \\ \\ Standard\text{ deviation = }√(1.66) \end{gathered}`
`Standard\text{ devaition = 1.29 \lparen2 decimal place\rparen}`