Question

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 Rht. 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

Let X denotes the number of students who have factor. the Rh the total Here number of students is n=7. Let denotes P that probability randomly selected student Rh factor. has Among undergraduate students donating blood ro walk-in clinic have Rh+ 30/ p 0.30

We assume that the students have Rh factor of each independently other. :X ~ Bin (n=7, p=0.30) The pmf of P(X=n) lo 0:30) 10.70) n=oll) 7 0 > W. Note that (7-x) denotes number of students the do not have the who Rh factor,

The probability that at Least three of them Rh do have factor the not = pl 7-X »3) el XE 7-3) plXEA) 2 11 P(x=0) + P(X=1) + P(x=2) P(x= 3) + P(x=4) 7-o 0.70) = 1) lº 10.30)° 10 7-1 + .) 1.383.0.507 13) 10.30) (0.70)-2 + (1) 10.303² (0.7000 06-30) 20-70) 7-3 7-4 +

+ = 0.082 354 + 0.247063 O. 317652 +0.22 68 95 + o. og 7 24 1 og 7 12. mean The true population is M = Elx) np 7 x 0.30 2.1

: The probability that the number of students with Rht blood be within of the true population 0.1 mean =pl lx-Mlson) = PI M-0.1 EXE M +0.1) = P(2.1-0.1 < x < 2.1 +0.1 1) e12eX = 2.2) P(x=2) 7- 2 2 1:10-30340707? 0.3177

2) the Let denotes n required number of undergraduate students. Let of У denotes the number students who have Rh factor the So, y ~ Bin (n. p=0.30) Y is : The pmf of ply=y) nay Slů (0.3 30) 910.70) y = olin 1 0.W.

Given that ply=1) > 0. go ply=1) = I-PlY21) 21 - ply=0) n - 0 ( 10.30)(0.70" 1) - 10.70" 1 - 10.70)" > 0.90 o.10 < a 10.70) nenlo.ro) a Inlo.10) nxl-0.3567) - 2.3026 > 0.3567n 2. 3026

2.3026 TA И 0.3567 6.46 n is always an integer so the minimum value of n is 7. 7 .. 7 undergraduate must donate students blood.