A local county has an unemployment rate of 4.4%. A random sample of 20 employable people are picked at random from the county and are asked if they are employed. Round answers to 4 decimal places.

Question

a) Find the probability that exactly 3 in the sample are unemployed.

Answer 1

unemployment rate = 4.4% = .044

a random sample of 20 is taken

what is the probability exactly 3 are unemployed?

exactly 0 unemployed would be probability = P(0) = 20C0(.956^20)(.044^0) = (.956^20)

exactly 1 unemployed: P(1) = 20C1(.956^19).044^1

exactly 2 unemployed P(2) = 20C2(.956^18)(.044^2)

exactly 3 unemployed: P(3)= 20C3(.956^17)(.044^3) = 20!/17!3!(.956^17)(.044^3) = (20)(19)(18)/(3)(2)(.956^17)(.044^3)

=1140(.956^17)(.044^3)

=about .04519049 = .0452 for 4 decimal places

= about 4.519049% = 4.519% for 4 decimal places

=chance of exactly 3 unemployed in a sample of 20 with 4.4% unemployment rate

= about .45% probability= slightly less than 1/2 %