The mean of a binomial distribution is
x, and the variance is 5 .
We know that the mean,
µ=np=x. This means
n times
p is
x.
The formula for variance is
σ2=np(1−p)=5. This means
n times
p times
(1−p) is 5 .
From the mean formula,
p=‌.
Substitute
p=‌ into the variance formula:
x(1−‌)=5If we open the bracket, we get:
x−‌=5Take
‌ to the other side:
‌=x−5Now, solve for
n :
n=‌To get a whole number for
n,x−5 must divide
x2 exactly. Let's check different
x values:
If
x=6:n=‌=3636 is an integer.
If
x=10:n=‌=2020 is an integer.
If
x=30:n=‌=3636 is an integer.
So, the possible values for
x are:
6,10,30.
