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=‌
x
n
. Substitute p=‌
x
n
into the variance formula: x(1−‌
x
n
)=5 If we open the bracket, we get: x−‌
x2
n
=5 Take ‌
x2
n
to the other side: ‌
x2
n
=x−5 Now, solve for n : n=‌
x2
x−5
To get a whole number for n,x−5 must divide x2 exactly. Let's check different x values: If x=6:n=‌
36
1
=3636 is an integer. If x=10:n=‌
100
5
=2020 is an integer. If x=30:n=‌
900
25
=3636 is an integer. So, the possible values for x are: 6,10,30.