# Binomial Distribution with non integer succes

I am doing a problem where I am to determine the probability that the number of students wanting a new book is within two standard deviations of the mean. μ +- 2δ comes out with a non integer number, in which I have to use to find probability. The equation to find probability uses the factorial of this number. Do I round this number to determine the factorial?

well if $\mu - 2 \delta$ is 12.3 and $\mu + 2 \delta$ is 17.8 then the number of students wanting the book is within two standard deviations of the mean when the number of students wanting the book is 13, 14, 15, 16, or 17. You can extrapolate.