A recent analysis of the number of rainy days per month found the following outcomes and probabilities: The standard deviation of this distribution is ___.
A) .800
B) .894
C) .400
D) 4.00
E) .457

Question

A recent analysis of the number of rainy days per month found the following outcomes and probabilities:  The standard deviation of this distribution is ___.
A) .800 
B) .894 
C) .400 
D) 4.00 
E) .457

Quizplus · Accepted Answer

To find the standard deviation, we need to calculate the variance first. We can use the formula σ^2=∑(x−μ)^2P(x), where σ is the standard deviation, μ is the mean, and P(x) is the probability of x.

From the table, we can see that the mean (μ) is 7, so we can calculate the variance as follows:

σ^2=((0−7)^2×0.1)+((1−7)^2×0.2)+((2−7)^2×0.3)+((3−7)^2×0.2)+((4−7)^2×0.1)=8.8

The standard deviation is the square root of the variance, so:

σ=√8.8=0.894

Therefore, the answer is choice B, 0.894.

A Recent Analysis of the Number of Rainy Days Per