Answer:
Mean = 8
Variance = 7.36
Standard Deviation = 2.7129
Step-by-step explanation:
This is a binomial distribution with parameters, n and p.
Where
n is sample size (given as 100)
p is the probability of success, or probability of defective (given as 8% or 0.08)
The mean, variance, standard deviation formula for binomial distribution is shown below:
Mean = [tex]np[/tex]
Variance = [tex]npq[/tex]
Standard Deviation = [tex]\sqrt{npq}[/tex]
Where q would be probability of failure, or "1 - p"
Thus,
n = 100
p = 0.08
q = 1 - 0.08 = 0.92
SO, we have:
Mean = [tex]np=100*0.08=8[/tex]
Variance = [tex]npq=100*0.08*0.92 = 7.36[/tex]
Standard Deviation = [tex]\sqrt{npq}=\sqrt{7.36}=2.7129[/tex]
