Score on last try: 0 of 1 pts. See Details for more.
Next question
$\rightleftarrows$ Get a similar question
You can retry this question below
\begin{tabular}{|l|r|}
\hline$x$ & $P(x)$ \\
\hline 0 & 0.15 \\
\hline 1 & 0.1 \\
\hline 2 & 0.25 \\
\hline 3 & 0.5 \\
\hline
\end{tabular}
5 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
Submit Question

Step 1 ：First, we need to calculate the mean of the distribution. The mean is calculated as \( \mu = \sum x_i * P(x_i) \).

Step 2 ：Given the values \( x_i = [0, 1, 2, 3] \) and the corresponding probabilities \( P(x_i) = [0.15, 0.1, 0.25, 0.5] \), we can calculate the mean as \( \mu = 2.1 \).

Step 3 ：Next, we calculate the standard deviation using the formula \( \sigma = \sqrt{\sum (x_i - \mu)^2 * P(x_i)} \).

Step 4 ：Substituting the values of \( x_i \), \( P(x_i) \), and \( \mu \) into the formula, we find that the standard deviation is \( \sigma = 1.0908712114635715 \).

Step 5 ：Rounding to at least 2 decimal places, the standard deviation of this probability distribution is \(\boxed{1.09}\).