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`

Explanation:

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

Mean =
`n\pi`

Standard deviation=
`√(n\pi(1-\pi))`

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

Mean =
`42*0.90=37.80`

Standard deviation=
`√(42(0.90)(0.10))=√(3.78)\approx1.9442`

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

Mean =
`80*0.70=56.00`

Standard deviation=
`√(80(0.70)(0.30))=√(16.8)\approx4.0988`

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

Mean =
`32*0.75=24`

Standard deviation=
`√(32(0.75)(0.25))=√(6)\approx2.4495`