Question

Find the mean and standard deviation for each binomial random variable:

Answer 1

Answer: a) Mean = $=37.80$

Standard deviation=$=1.9442$

b) Mean = $56.00$

Standard deviation=$4.0988$

c) Mean = $=24$

Standard deviation=$2.4495$

Step-by-step explanation:

To compute Mean and standard deviation , we use following formula:

Mean = $n\pi$

Standard deviation=$\sqrt{n\pi(1-\pi)}$

a. $n=42,\ \pi=0.90$

Mean = $42\times0.90=37.80$

Standard deviation=$\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442$

b. $n=80,\ \pi=0.70$

Mean = $80\times0.70=56.00$

Standard deviation=$\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988$

c. $n=32,\ \pi=0.75$

Mean = $32\times0.75=24$

Standard deviation=$\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495$