For a binomial distribution with n = 100,which of the following has the largest standard deviation?
A)p = 0.50
B)p = 0.20
C)p = 0.10
D)p = 0.05

Question

For a binomial distribution with n = 100,which of the following has the largest standard deviation?​
A)​p = 0.50
B)p = 0.20​
C)​p = 0.10
D)​p = 0.05

Quizplus · Accepted Answer

The formula for the standard deviation of a binomial distribution is √(np(1-p)), where n is the number of trials and p is the probability of success on each trial.

For all choices, n = 100.

Calculating the standard deviation for each choice: 
A) √(100*0.50*(1-0.50)) = 5 
B) √(100*0.20*(1-0.20)) ≈ 3.16 
C) √(100*0.10*(1-0.10)) ≈ 3.00 
D) √(100*0.05*(1-0.05)) ≈ 2.17

Therefore, choice A (p = 0.50) has the largest standard deviation of 5.

For a Binomial Distribution with N = 100,which of the Following