Home > Statistics > Calculating Binomial Probabilities

What is the variance of a binomial distribution for which n = 75 and p = 0.20?

Answer 1

75 x #(1/5)# x #(4/5)#

The formula for the variance of a binomial distribution is n x p x q where q = 1 - p. Here n = 75, p = .20 or #(1/5)# and q = 0.80 or #(4/5)# and hence the answer.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emery Adams

The answer is #12#.

Note that if #X~ "Bin ( n , p )"# then Variance of #X# is #np(1-p)#.

Now your # n = 75 # and # p = 0.20 #.

So your variance = # 75 times 0.20 times ( 1 - 0.20 ) = 75 times 0.20 times 0.80 =12#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Hailey Anderson

The variance of a binomial distribution is given by the formula ( \text{Var}(X) = np(1 - p) ), where ( n ) is the number of trials and ( p ) is the probability of success on each trial.

Substituting ( n = 75 ) and ( p = 0.20 ) into the formula:

[ \text{Var}(X) = 75 \times 0.20 \times (1 - 0.20) = 75 \times 0.20 \times 0.80 ]

[ \text{Var}(X) = 15 \times 0.80 = 12 ]

So, the variance of the binomial distribution with ( n = 75 ) and ( p = 0.20 ) is ( 12 ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.