A market research team compiled the following discrete probability distribution.In this distribution x represents the number of automobiles owned by a family. The standard deviation of x is ___.
A)0.80
B)0.89
C)1.00
D)2.00
E)2.25

Question

A market research team compiled the following discrete probability distribution.In this distribution x represents the number of automobiles owned by a family.  The standard deviation of x is ___.
A)0.80 
B)0.89 
C)1.00 
D)2.00 
E)2.25

Quizplus · Accepted Answer

To calculate the standard deviation of a discrete probability distribution, we use the formula:

sqrt(sum((x-mean)^2*p(x)))

where x is the value of the variable, p(x) is the corresponding probability, and mean is the expected value (which in this case is 1.5).

Using this formula, we get:

sqrt(((0-1.5)^2*0.20) + ((1-1.5)^2*0.35) + ((2-1.5)^2*0.25) + ((3-1.5)^2*0.10) + ((4-1.5)^2*0.10))

= sqrt(0.36 + 0.1225 + 0.0625 + 0.0225 + 0.0225)

= sqrt(0.605)

≈ 0.89

Therefore, the standard deviation of x is 0.89, which is closest to choice B.

A Market Research Team Compiled the Following Discrete Probability Distribution