question number 6. (10.00 points) in testing a certain kind of missile, target accuracy is measured by the average distance x (from the target) at which the missile explodes. the distance x is measured in miles and the sampling distribution of x is given by:
|x|p(x)|
|----|----|
|0|1/12|
|10|1/6|
|50|1/3|
|100|5/12|
calculate the variance of this sampling distribution.
1416.7
472.2
60.0
2800.0
37.6
none of the above

Question

Accepted Answer

# Explanation:
## Step1: Recall variance formula for discrete - random variable
The formula for the variance of a discrete - random variable $X$ is $Var(X)=\sum_{i}(x_{i}-\mu)^{2}P(x_{i})$, where $\mu = E(X)=\sum_{i}x_{i}P(x_{i})$. First, find the expected value $\mu$.
$$
\begin{align*}
E(X)&=\sum_{i}x_{i}P(x_{i})\
&=0\times\frac{1}{12}+ 10\times\frac{1}{6}+50\times\frac{1}{3}+100\times\frac{5}{12}\
&=0+\frac{10}{6}+\frac{50}{3}+\frac{500}{12}\
&=\frac{20 + 200+500}{12}\
&=\frac{720}{12}\
& = 60
\end{align*}
$$
## Step2: Calculate variance
$$
\begin{align*}
Var(X)&=(0 - 60)^{2}\times\frac{1}{12}+(10 - 60)^{2}\times\frac{1}{6}+(50 - 60)^{2}\times\frac{1}{3}+(100 - 60)^{2}\times\frac{5}{12}\
&=3600\times\frac{1}{12}+2500\times\frac{1}{6}+100\times\frac{1}{3}+1600\times\frac{5}{12}\
&=300+\frac{1250}{3}+\frac{100}{3}+\frac{2000}{3}\
&=300+\frac{1250 + 100+2000}{3}\
&=300+\frac{3350}{3}\
&=\frac{900+3350}{3}\
&=\frac{4250}{3}\approx1416.7
\end{align*}
$$
# Answer:
1416.7

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QUESTION IMAGE

Question

Explanation:

Step1: Recall variance formula for discrete - random variable

Step2: Calculate variance

Answer:

x	p(x)
10	1/6
50	1/3
100	5/12