Question

use the probability distribution to complete parts (a) and (b) below.

the number of school - related extracurricular activities per student
activities 0 1 2 3 4 5 6 7
probability 0.058 0.124 0.163 0.178 0.214 0.128 0.083 0.052

(a) find the mean, variance, and standard deviation of the probability distribution.
the mean is 3.3.
(round to one decimal place as needed.)
the variance is 3.4.
(round to one decimal place as needed.)
the standard deviation is
(round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation ($\sigma$) of a probability distribution is the square root of the variance ($\sigma^2$). The formula is $\sigma = \sqrt{\sigma^2}$.

Step2: Substitute the variance value

We know the variance ($\sigma^2$) is 3.4. So we calculate the square root of 3.4.
$\sigma = \sqrt{3.4} \approx 1.8$ (rounded to one decimal place)

Answer:

1.8