Question

If x is a binomial random​ variable, calculate muμ​, sigma squaredσ2​, and sigmaσ for each of the following values of n and p. Complete parts a through f.

a.) n=30, p=0.5

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed..

b.) n=82, p=0.2

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed.

c.) n=105 p=0.6

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed.)

d.) n=67 p=0.9

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed.)

e.) n=63, p=0.8

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed.)

f.) n=900,p=0.06

muμequals=nothing

​(Round to the nearest tenth as​ needed.)

sigma squaredσ2equals=nothing

​(Round to the nearest hundredth as​ needed.)

sigmaσequals=nothing

​(Round to the nearest thousandth as​ needed.)

Answer 1

Part a)

Mean = n * P = ( 30 * 0.5 ) = 15
Variance = n * P * Q = ( 30 * 0.5 * 0.5 ) = 7.50
Standard deviation = = 2.739

Part b)

Mean = n * P = ( 82 * 0.2 ) = 16.4
Variance = n * P * Q = ( 82 * 0.2 * 0.8 ) = 13.12
Standard deviation = = 3.622

Part c)

Mean = n * P = ( 105 * 0.6 ) = 63
Variance = n * P * Q = ( 105 * 0.6 * 0.4 ) = 25.20
Standard deviation = = 5.020

Part d)

Mean = n * P = ( 67 * 0.9 ) = 60.3
Variance = n * P * Q = ( 67 * 0.9 * 0.1 ) = 6.03
Standard deviation = = 2.457

Part e)

Mean = n * P = ( 63 * 0.8 ) = 50.4
Variance = n * P * Q = ( 63 * 0.8 * 0.2 ) = 10.08
Standard deviation = = 3.175

Part f)

Mean = n * P = ( 900 * 0.06 ) = 54
Variance = n * P * Q = ( 900 * 0.06 * 0.94 ) = 50.76
Standard deviation =   = 7.125