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:

p(x)	x
1/14	10
1/2	50
3/4	100

calculate the mean of this sampling distribution.
o 85.4
o 31.6
o 81.4
o 899.0
o 82.9
o none of the above

Explanation:

Step1: Recall mean - formula for discrete distribution

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

Step2: Calculate the product for each pair

For $x_1 = 0$ and $p_1=\frac{1}{28}$, the product $x_1p_1=0\times\frac{1}{28} = 0$.
For $x_2 = 10$ and $p_2=\frac{1}{14}$, the product $x_2p_2=10\times\frac{1}{14}=\frac{10}{14}=\frac{5}{7}$.
For $x_3 = 50$ and $p_3=\frac{1}{2}$, the product $x_3p_3=50\times\frac{1}{2}=25$.
For $x_4 = 100$ and $p_4=\frac{3}{4}$, the product $x_4p_4=100\times\frac{3}{4}=75$.

Step3: Sum up the products

$\mu=0+\frac{5}{7}+25 + 75$.
First, find a common denominator. The common denominator of 1 and 7 is 7.
$\mu=\frac{0 + 5+175+525}{7}=\frac{705}{7}\approx85.4$.

Answer:

85.4