25 children in a class each roll a fair die 30 times and record the number of sixes they obtain. Find an estimate of the probability that the mean number of sixes recorded for the class is less than 4.5.

I have worked out the mean [tex] E(x) = /frac{7}{2} [\tex] do I multiply this by 25?

also I tried to calculate the variance using this formula [tex] Var(X) = E(X^{2}) - E(X)^{2} [\tex] but get a negative answer.

I square all the the numbers 1-6 on the die, and than multiply my their probability and each number has 1/6 chance.

[tex] Var(X) = 1^{2} x /frac{1}{6} + 2^{2} x /frac{1}{6} + 3^{2} x/frac{1}{6} + 4^{2} x /frac{1}{6} + 5^{2} x /frac{1}{6} + 6^{2} x /frac{1}{6} - /frac{7}{2}^{2} [\tex]

=

I know i have to use the formula [tex] Z = /frac{y- /mu}{/sigma} [\tex]