Question

question number 3. (10.00 points) given the following sampling distribution: what is the mean of this sampling distribution? -0.2 -3.2 9.0 9.2 8.9 none of the above

p(x)	x
9/100	-14
7/100	-3
2/25	5
	15

Explanation:

Step1: Recall mean formula for discrete - distribution

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

Step2: Calculate the products

For $x_1=-19$ and $p_1 = \frac{1}{25}=0.04$, the product $x_1p_1=-19\times0.04=- 0.76$.
For $x_2=-14$ and $p_2=\frac{9}{100}=0.09$, the product $x_2p_2=-14\times0.09=-1.26$.
For $x_3=-3$ and $p_3=\frac{7}{100}=0.07$, the product $x_3p_3=-3\times0.07 = - 0.21$.
For $x_4 = 5$ and $p_4=\frac{2}{25}=0.08$, the product $x_4p_4=5\times0.08 = 0.4$.
Let the probability of $x_5 = 15$ be $p_5$. Since the sum of all probabilities in a probability - distribution is 1, we first find $p_5$.
$p_5=1-(0.04 + 0.09+0.07 + 0.08)=1 - 0.28=0.72$.
The product $x_5p_5=15\times0.72 = 10.8$.

Step3: Sum up the products

$\mu=-0.76-1.26-0.21 + 0.4+10.8$.
$\mu=-2.23+0.4 + 10.8$.
$\mu=-1.83+10.8$.
$\mu = 8.97\approx8.9$.

Answer:

8.9