Mathematics, 12.07.2021 22:40 lachlyn40

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities. (a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Round your answers to two decimal places (e. g. 98.76).

Answers: 2

Show answers

Answers

Answer from: krystalhurst97

a) 0.6730 = 67.30% probability that no samples are mutated.

b) 0.9436 = 94.36% probability that at most one sample is mutated.

c) 0% probability that more than half the samples are mutated.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either it is mutated, or it is not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used 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.

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases.

This means that p = 0.03

13 samples are studied

This means that n = 13

(a) No samples are mutated.

This is P(X = 0). So

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

$P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730$

0.6730 = 67.30% probability that no samples are mutated.

(b) At most one sample is mutated.

This is:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730$

$P(X = 1) = C_{13,1}.(0.03)^{1}.(0.97)^{12} = 0.2706$

Then

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.6730 + 0.2706 = 0.9436$

0.9436 = 94.36% probability that at most one sample is mutated.

This is:

P(X 6.5) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)

Then

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

$P(X = 7) = C_{13,7}.(0.03)^{7}.(0.97)^{6} \approx 0$

Using two decimal digits precision, all will be 0. So

0% probability that more than half the samples are mutated.

Answer from: Quest

Ithink number to is 1 inch=5 miles
This is the picture of the homework

Answer from: Quest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

Another question on Mathematics

Mathematics, 21.06.2019 14:10

Abaker makes 186 cookies. some are chocolate chip and some are oatmeal raisin, and both kinds are made with and without nuts, as shown in the table above. because they are more popular, the baker made 2/3 of the cookies chocolate chip. if a chocolate chip cookie is chosen at random, what is the probability that it will have nuts? a) 21/93 b) 21/62 c) 41/93 d) 21/41

Answers: 2

Answer

Mathematics, 21.06.2019 15:30

The area of a rectangle is 15+5y square feet. which of the following expressions could be the length of the sides of the rectangle, in feet a. 5 and 3y b. 5 and 3+y c. 5 and 5+y d. 3 and 5+3y

Answers: 1

Answer

Mathematics, 21.06.2019 15:40

What term best describes a line ans a point that lie in the same plane

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8

Answers: 2

Answer

You know the right answer?

Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are s...

Questions