Question

Math Problem Solving
statistics and probability​

Answer 1

Standard Deviation = 3.22

Variance = 10.36

Explanation:

x P(x) x × P(x) x² x² × P(x)

19 0.20 3.8 361 72.2

10 0.20 2 100 20

11 0.30 3.3 121 36.3

12 0.20 2.4 144 28.8

13 0.10 1.3 169 16.9

____________________________________________

12.8 174.2 => Total

Mean Formula

`\mu_x = \sum(x * P(x))`
`= 12.8`

`\mu_x^2 = 163.84`

Variance Formula

`\sigma _x^2 = \sum[x^2 * P(x)] - \mu_x^2`

`= 174.2- 163.84\\\\=10.36`

Standard Deviation Formula

`Standard\ deviation, \ \sigma_x = √(Variance)`

`=√(10.36)\\\\=3.218`