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. 81.4 999.0 85.4 31.6 82.9 none of the above

Explanation:

Step1: Recall the formula for the mean of a discrete - probability distribution

The formula for the mean $\mu$ of a discrete - probability distribution is $\mu=\sum_{i}x_ip_i$, where $x_i$ are the possible values of the random variable and $p_i$ are their corresponding probabilities.

Step2: Calculate the product of each $x$ and $p$ value

For $x = 0$ and $p=\frac{1}{28}$, the product is $0\times\frac{1}{28}=0$.
For $x = 10$ and $p=\frac{1}{14}$, the product is $10\times\frac{1}{14}=\frac{10}{14}=\frac{5}{7}\approx0.714$.
For $x = 50$ and $p=\frac{1}{7}$, the product is $50\times\frac{1}{7}=\frac{50}{7}\approx7.143$.
For $x = 100$ and $p=\frac{3}{4}$, the product is $100\times\frac{3}{4}=75$.

Step3: Sum up the products

$\mu=0+\frac{5}{7}+\frac{50}{7}+75=\frac{5 + 50}{7}+75=\frac{55}{7}+75=\frac{55}{7}+\frac{525}{7}=\frac{55 + 525}{7}=\frac{580}{7}\approx82.9$

Answer:

82.9