The mean, variance, and standard deviation of a binomial distribution with parameters n and p are:
[tex]\begin{gathered} \operatorname{mean}=n\cdot p \\ \text{variance = n}\cdot p\cdot(1-p) \\ \text{ Standard deviation =}\sqrt[]{n\cdot p\cdot(1-p)} \end{gathered}[/tex]
So, replacing the values of n and p, we get:
[tex]\begin{gathered} \operatorname{mean}=128\cdot0.49=62.72 \\ \text{variance}=128\cdot0.49\cdot(1-0.49)=31.9872 \\ \text{ standard deviation = }\sqrt[]{31.9872}=5.6557 \end{gathered}[/tex]
Answer: mean = 62.72
variance = 31.9872
standard deviation = 5.6557
