Question

Please help me as soon as you can! Thank you soooooo much!

Exercice 3: Rhesus factor, is a type of protein found on the outside of red blood cells. The protein is genetically inherited. A donor is said to have Rh+ blood if the Rhesus factor is present in their blood. Suppose that a blood donation campaign is launched by the University of Ottawa walk-in clinic. Among undergraduate students donating blood to walk-in clinic, 30% have Rh+. 1. If seven undergraduate students donate blood at this clinic on a particular day, what is the probability that at least three of them do not have the Rh factor? What is the probability that the number of students with Rh+ blood will be within 0.1 of the true population mean? 2. How many undergraduate students must donate blood to have the prob- ability of at least one Rh+ donor over 0.90?

Answer 1

1)

a)

here this is binomial with parameter n=7 and p=0.3

P(at least 3 does not have RH factor) =P(at most 4 have Rh factor)

=P(X<=2)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

=C(7,0)*(0.3)^0*(0.7)^7+C(7,1)*(0.3)^1*(0.7)^6+C(7,2)*(0.3)^2*(0.7)^5+C(7,3)*(0.3)^3*(0.7)^4+C(7,4)*(0.3)^4*(0.7)^3

=0.9712

b)

P(within 0.1 of true population mean)=P(0.2<x/n<0.4)=P(0.2*7<X<0.4*7)=P(1.4<X<2.8)

=P(X=2)=C(7,2)*(0.3)^2*(0.7)^5 =0.3177

b)

let number of undergraduate are a;

P(at least one have Rh+)=1-P(none have) =1-0.7^a =0.9

0.7^a =0.1

a =ln(0.1)/ln(0.7)= 6.46 ~ 7 (rounding up)