Mathematics, 28.02.2021 16:20 quay39

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U. S. residents and 40 Australians is obtained. Consider the random variables described below: X: the number of US residents (out of 50) with blood type AB.
Y: the number of Australians (out of 40) with blood type AB.
Z: the total number of individuals (out of 90) with blood type AB.

Which of the following is true about the random variables X, Y, and Z?

a. X is a binomial random variable with n = 50 and p = 0.04
b. Y is a binomial random variable with n = 40 and p = 0.015
c. Z is a binomial random variable with n = 90 and p = 0.055

Answers: 2

Show answers

Answers

Answer from: carethegymnast8954

a. X is a binomial random variable with n = 50 and p = 0.04

b. Y is a binomial random variable with n = 40 and p = 0.015

Step-by-step explanation:

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.

X: the number of US residents (out of 50) with blood type AB.

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States

This means that p = 0.04, n = 50

Y: the number of Australians (out of 40) with blood type AB.

In Australia, only 1.5% of the population has blood type AB.

This means that p = 0.015, n = 40

Z: the total number of individuals (out of 90) with blood type AB.

Here

$n = 90, p = 0.04*\frac{50}{90} + 0.015*\frac{40}{90} = 0.0289$

Which of the following is true about the random variables X, Y, and Z?

Options a and b are true, while c is false.

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

step-by-step explanation:

compare

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:20, ellenharley7

What value of x is in the solution set of 4x - 12 s 16 + 8x? -10 -9 -8 -7

Answers: 1

continue

Mathematics, 21.06.2019 18:30, ekayla163

Find an equation of the line perpendicular to the graph of 28x-7y=9 that passes through the point at (4,1)

Answers: 2

continue

Mathematics, 21.06.2019 20:00, naimareiad

Ialready asked this but i never got an answer. will give a high rating and perhaps brainliest. choose the linear inequality that describes the graph. the gray area represents the shaded region. y ≤ –4x – 2 y > –4x – 2 y ≥ –4x – 2 y < 4x – 2

Answers: 1

continue

Mathematics, 21.06.2019 21:30, peytonamandac9114

Ahypothesis is: a the average squared deviations about the mean of a distribution of values b) an empirically testable statement that is an unproven supposition developed in order to explain phenomena a statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order da statement that is the opposite of the null hypothesis e) the error made by rejecting the null hypothesis when it is true

Answers: 2

continue

You know the right answer?

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States....