Question

According to the National Work Intensification Survey, 42% of Americans felt their workload last year had significant more responsibility when compared to the start of the recession in December 2007. A random sample of five working Americans was selected. Question One: What is the probability that none of them felt their workload last year had significant more responsibility? Question Two: What is the probability that more than three of them felt their workload last year had significant more responsibility? Question Three: What is the probability that one or two of them felt their workload last year had significant more responsibility?

Answer 1

Solution-1;

p=0.42

n=5

q=1-p=1-0.42=0.58

P(X=0)

From binomial distribution

P(X=x)=ncx*p^x*q^n-x

P(X=0)=5c0*0.42^0*0.58^5-0

= 0.06563568

WITH EXCEL FORMULA ALSO YOU CAN GET ANSWER

=BINOM.DIST(0,5,0.42,FALSE)

=0.0656

ANSWER:

0.0656

(rounded to 4 decimals)

Solution-2:

P(X>3)

=P(X=4)+P(X=5)

=0.09023918+ 0.01306912

=0.1033083

=0.1033

EXCEL FORMULA

=BINOM.DIST(4,5,0.42,FALSE)+=BINOM.DIST(5,5,0.42,FALSE)

=0.0902+0.0131

=0.1033

ANSWER:

0.1033

(rounded to 4 decimals)

Solution-3:

P(X=1)+P(X=2)

0.2376464+ 0.3441776

=0.581824

=0.5818

EXCEL FORMULA:

=BINOM.DIST(1,5,0.42,FALSE)+=BINOM.DIST(2,5,0.42,FALSE)

=0.2376+0.3442

ANSWER

0.5818

(rounded to 4 decimals)