Question

question number 5. (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. calculate the mean of this sampling distribution. 1416.7 37.6 58.5 62.5 60.0 none of the above

Explanation:

Step1: Recall mean formula

The mean $\mu$ of a discrete - probability distribution is given by $\mu=\sum_{i}x_ip(x_i)$.

Step2: Calculate the product for each pair

For $x = 0$ and $p(x)=\frac{1}{12}$, the product is $0\times\frac{1}{12}=0$.
For $x = 10$ and $p(x)=\frac{1}{6}$, the product is $10\times\frac{1}{6}=\frac{10}{6}=\frac{5}{3}$.
For $x = 50$ and $p(x)=\frac{1}{3}$, the product is $50\times\frac{1}{3}=\frac{50}{3}$.
For $x = 100$ and $p(x)=\frac{5}{12}$, the product is $100\times\frac{5}{12}=\frac{500}{12}=\frac{125}{3}$.

Step3: Sum up the products

$\mu=0+\frac{5}{3}+\frac{50}{3}+\frac{125}{3}=\frac{5 + 50+125}{3}=\frac{180}{3}=60$.

Answer:

60.0