The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first $g$ | class is shown below.
$\begin{array} { l l l l l l l } \text { Number of cartoons watched } \boldsymbol { X } & 0 & 1 & 2 & 3 & 4 & 5 \ \text { Probability } \boldsymbol { P } ( \boldsymbol { X } ) & 0.15 & 0.20 & 0.30 & 0.10 & 0.20 & 0.05 \end{array}$
Give the standard deviation for the probability distribution. de
A) 1.46
B) 1.89
C) 1.18
D) 2.25

Question

Quizplus · Accepted Answer

The standard deviation of a probability distribution is calculated using the formula $\sigma = \sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)}$, where $\mu$ is the mean of the distribution. First, calculate the mean: $\mu = \sum x_i \cdot P(x_i) = 0(0.15) + 1(0.20) + 2(0.30) + 3(0.10) + 4(0.20) + 5(0.05) = 2.05$. Then, calculate the variance: $\sigma^2 = (0-2.05)^2(0.15) + (1-2.05)^2(0.20) + (2-2.05)^2(0.30) + (3-2.05)^2(0.10) + (4-2.05)^2(0.20) + (5-2.05)^2(0.05) = 2.1475$. Finally, the standard deviation $\sigma = \sqrt{2.1475} \approx 1.46$.

The Number of Cartoons Watched on Saturday Mornings by Students ggg

The Number of Cartoons Watched on Saturday Mornings by Students $g$