Examine the following probability distribution:
The range and standard deviation of the distribution are:
A)$4000 and $1095.45,respectively.
B)$1095.45 and $4000,respectively.
C)$5000 and $1095.45,respectively.
D)$4000 and $2000,respectively.

Question

Examine the following probability distribution: 
The range and standard deviation of the distribution are:
A)$4000 and $1095.45,respectively. 
B)$1095.45 and $4000,respectively. 
C)$5000 and $1095.45,respectively. 
D)$4000 and $2000,respectively.

Quizplus · Accepted Answer

To find the range, we simply subtract the minimum value from the maximum value: $9000 - $500 = $4000. To find the standard deviation, we need to use the formula: 
$\sigma = \sqrt{\sum(x-\mu)^2 \cdot P(x)}$ 
where $\mu$ is the mean of the distribution. From the table, we can find that the mean is: 
$\mu = 0.2(500) + 0.4(1000) + 0.3(1500) + 0.1(2000) = 1070$
Using this, we can calculate the standard deviation: 
$\sigma = \sqrt{(500-1070)^2 \cdot 0.2 + (1000-1070)^2 \cdot 0.4 + (1500-1070)^2 \cdot 0.3 + (2000-1070)^2 \cdot 0.1}$
$\sigma \approx 1095.45$
Therefore, the correct answer is A.

Examine the Following Probability Distribution