Respuesta :
Answer:
a) 0.3226
b) 0.9340
c) 0.5257
d) mean=1.68 workers , standard deviation=1.15 workers
Step-by-step explanation:
since each worker's gender is independent from the others , then defining the random variable X= getting x male workers out of the sample of 8 workers , we know that P(X) has a binomial distribution , where
P(X)=n!/((n-x)!*x!)*p^x*(1-p)^(n-x)
where
n= sample size = 8
p= probability that a worker is male = 0.21
x= x workers are male
then
a) P(X=1) = 8!/((8-1)!*1!)*(0.21)^1*(1-0.21)^(8-1) = 0.3226
b) P(X<4) = P(X=0) + P(X=1)+ P(X=2)+ P(X=3) + P(X=4)
in order to avoid doing the calculus for each term we can use the cumulative probability distribution , whose results can be found in tables. Then
P(X<4)= F(4) = 0.9340
c) P(X>2) = 1- P(X≤1) = 1- F(1) = 1- 0.4743 = 0.5257
d) the mean for a binomial distribution is
E(X)= n*p = 8*0.21 = 1.68 workers
and the standard deviation is
σ(X)= √[n*p*(1-p)]= √[8*0.21*0.79]= 1.15 workers
