Question

section 6.1 homework score: 7.92/21 answered: 9/21 question 11 score on last try: 0.25 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable in > next question get a similar question you can retry consider the discrete random variable x given in the table below. standard deviation of x. round answers to two decimal places.

x	3	10	12	14	19
p(x)	0.13	0.59	0.12	0.08	0.08

μ = 10.37
σ² =
σ =
what is the expected value of x? enter an integer or decimal number more...

Explanation:

Step1: Recall expected - value formula

The expected value $\mu$ (already given as correct: $\mu=\sum_{i}x_ip_i$) of a discrete random variable $X$ with values $x_i$ and probabilities $p_i$ is calculated as $\mu = 3\times0.13+10\times0.59 + 12\times0.12+14\times0.08+19\times0.08=0.39 + 5.9+1.44 + 1.12+1.52=10.37$.

Step2: Recall variance formula

The variance $\sigma^{2}=\sum_{i}(x_i - \mu)^{2}p_i$.
$(3 - 10.37)^{2}\times0.13=( - 7.37)^{2}\times0.13 = 54.3169\times0.13 = 7.061197$.
$(10 - 10.37)^{2}\times0.59=( - 0.37)^{2}\times0.59 = 0.1369\times0.59 = 0.080771$.
$(12 - 10.37)^{2}\times0.12=(1.63)^{2}\times0.12 = 2.6569\times0.12 = 0.318828$.
$(14 - 10.37)^{2}\times0.08=(3.63)^{2}\times0.08 = 13.1769\times0.08 = 1.054152$.
$(19 - 10.37)^{2}\times0.08=(8.63)^{2}\times0.08 = 74.4769\times0.08 = 5.958152$.
$\sigma^{2}=7.061197+0.080771 + 0.318828+1.054152+5.958152=14.47309$.

Step3: Recall standard - deviation formula

The standard deviation $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{14.47309}\approx3.80$.

Answer:

$\sigma^{2}=14.47$
$\sigma = 3.80$