Mathematics, 24.06.2020 09:01 heroicblad

Blood types: The blood type o negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type o negative blood. For this
reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U. S.
residents have type o negative blood. Assume that a blood bank has recruited 18 donors. Round the answers to four decimal places
Part 1 of 3
(a) What is the probability that three or more of them have type o negative blood?
The probability that three or more of them have type o negative blood is
х
Part 2 of 3
(b) What is the probability that fewer than five of them have type o negative blood?
The probability that fewer than five of them have type o negative blood is
х
Part 3 of
(©) Would it be unusual f none of the donors had type o negative blood?
be unusual if none of the donors had type o negative blood since the probability is
X
It choose one) Y
would
would not

Answers: 2

Show answers

Answers

Answer from: moisesnunez408

a) The probability that fewer than five of them have type o negative blood is 0.1275

b) The probability that fewer than five of them have type o negative blood is 0.9933

c) 0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type o negative blood, or they do not. The probability of a person having type o negative blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

7% of U.S. residents have type o negative blood.

This means that p = 0.07

18 donors.

This means that n = 18

(a) What is the probability that three or more of them have type o negative blood?

Either less than three have, or at least three do. The sum of the probabilities of these events is 1. So

$P(X < 3) + P(X \geq 3) = 1$

We want $P(X \geq 3)$

$P(X \geq 3) = 1 - P(X < 3)$

In which

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

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708$

$P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669$

$P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348$

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2708 + 0.3669 + 0.2348 = 0.8725

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.8725 = 0.1275$

The probability that fewer than five of them have type o negative blood is 0.1275

(b) What is the probability that fewer than five of them have type o negative blood?

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708$

$P(X = 1) = C_{18,1}.(0.07)^{1}.(0.93)^{17} = 0.3669$

$P(X = 2) = C_{18,2}.(0.07)^{2}.(0.93)^{16} = 0.2348$

$P(X = 3) = C_{18,3}.(0.07)^{3}.(0.93)^{15} = 0.0942$

$P(X = 4) = C_{18,4}.(0.07)^{4}.(0.93)^{14} = 0.0266$

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.2708 + 0.3669 + 0.2348 + 0.0942 + 0.0266 = 0.9933

The probability that fewer than five of them have type o negative blood is 0.9933.

c) Would it be unusual f none of the donors had type o negative blood?

$P(X = 0) = C_{18,0}.(0.07)^{0}.(0.93)^{18} = 0.2708$

0.2708 probability of no donors with type o negative blood. This probability is higher than 0.05, so it would not be unusual having none of the donors with type o negative blood.

Answer from: Quest

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

Answer from: Quest

answer: y = -2.5x - 15

(-6,0)

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 14:00

Lorenzo ate 2/5 of his bag of almonds. his 4 friends ate equal shares of the remaining bag of almonds?

Answers: 1

Answer

Mathematics, 21.06.2019 16:40

What is the average rate of change for this function for the interval from x=2 to x=4 ?

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

Sasha drank 8 bottles of water everyday for a week. how many bottles of water did she drink in total?

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

This circle is centered at the origin, and the length of its radius is 6. what is the circle's equation? a. x^2+y^2=36 b x^2+y^2=6 c x+y=36 d x^6+y^6=1

Answers: 2

Answer

You know the right answer?

Blood types: The blood type o negative is called the "universal donor" type, because it is the only...

Questions