Question

A recent survey taken by Adecco of 1,047 employees found that 28% of them would lay off their bosses if they could. Answer the following questions based on a random sample of 10 employees. a. What is the probability that exactly three employees would lay off their bosses? b. What is the probability that three or fewer employees would lay off their bosses? c. What if the probability that five or more employees would lay off their bosses? d. What are the mean and standard deviation for this distribution? e. Construct a histogram for this distribution..

Answer 1

here this is binomial with parameter n=10 and p=0.28

a)

P(X=3)=

(nCx)px(1−p)(n-x)    =

0.2642

b)

P(X<=3)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.7021

c)

P(X>=5)=1-P(X<=4)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1181

d)

mean E(x)=μ=np=2.8

standard deviation σ=√(np(1-p))=1.4199