Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!)

A)0.25
B)0.50
C)0.75
D)1.00

Question

Without writing down any calculations, determine the mean of the distribution shown. The variance of this probability distribution is (you can do this in your head!)

A)0.25 
B)0.50 
C)0.75 
D)1.00

Quizplus · Accepted Answer

Since the variance of a binomial distribution with parameters n and p is np(1-p), we can determine that np(1-p) = 0.25. Since the variance is equal to np(1-p), we know that np = 0.5 (since 0.5 x 0.5 = 0.25). Therefore, the mean is np/p = n = 0.5/0.5 = 1.0. Therefore, the best choice is B) 0.50. Since the variance of the distribution is given and we know that $	ext{Var}(X) = E(X^2) - [E(X)]^2$, we can easily find the mean by rearranging the formula as $E(X) = \sqrt{	ext{Var}(X) + [E(X)]^2}$. Since the options only differ by 0.25, we can quickly eliminate options A and D since their means would be too small or too large, respectively, for the given variance. Option C is also too large since the maximum value of the distribution is 1. Therefore, the only option left is B, and we can check that its mean satisfies the formula above.

Without Writing Down Any Calculations, Determine the Mean of the Distribution