Question

the following table represents the probability distribution of the number of vacations X taken last year for a randomly chosen family. compute the standard deviation

Answer 1

We have to use the formula for standard deviation of a probability distribution:

`\sigma=\sqrt[]{\sum^{}_(i\mathop=0)(x_i-\mu)^2\cdot P(x_i)}`

x P(x) x*P(x) (xi - μ)^2*P(x)

0 0.11 0 0.180

1 0.64 0.64 0.050

2 0.13 0.26 0.067

3 0.1 0.3 0.296

4 0.02 0.08 0.148

The expected value μ would be the sum of the values of the third column of the table.

Therefore μ = 1.28

The sum of the values of the fourth column would be: 0.7416

Taking the square root of the last value, we have: 0.861

The answer is option D