Mathematics, 17.11.2019 12:31 jaanne

Arecent harvard study shows that approximately 12% of americans are left‑handed. suppose alex takes a random sample of four americans. what is the probability that at least one american is left‑handed or at least three americans are right‑handed?

Answers: 2

Show answers

Answers

Answer from: blaze9691

A. The probability of at least one American is left-handed is 92.68% for a sample of 4 random Americans.

B. The probability of at least three Americans are right-handed is 7.32% for a sample of 4 random American

Step-by-step explanation:

This is a binomial distribution study where n = 4 and p = 0.12. Using the binomial table, where the first column is the distribution function, f(x), and the second is the cumulative distribution function F(x), we can calculate the probabilities.

00.59970.5997

10.32710.9268

20.06690.9937

30.00610.9998

40.00021.0000

Now, we can answer the questions, this way:

A. What is the probability that at least one American is left‑handed?

P (0) + P (1) = 0.5997 + 0.3271 = 0.9268

The probability of at least one American is left-handed is 92.68% for a sample of 4 random Americans.

B. What is the probability that at least three American are right‑handed?

1 - P(0) - P(1) = 1 - 0.5997 - 0.3271 = 0.0732

The probability of at least three Americans are right-handed is 7.32% for a sample of 4 random Americans.

Answer from: lexiepedit4958

132.71% probability that at least one American is left‑handed or at least three Americans are right‑handed

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they are right handed, or they are left handed. The probability of a person being left or right handed 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.

Sample of four:

This means that n = 4

At least one left-handed

12% are left handed, so p = 0.12.

Either there are no left handed people in the sample, or there is at least one. The sum of the probabilities of these events is decimal 1. So

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

We want $P(X \geq 1)$ , so

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5997 = 0.4003$

At least three right-handed:

100-12 = 88% are right handed, so p = 0.88.

$P(X \geq 3) = P(X = 3) + P(X = 4)$

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

$P(X = 3) = C_{4,3}.(0.88)^{3}.(0.12)^{1} = 0.3271$

$P(X = 4) = C_{4,4}.(0.88)^{4}.(0.12)^{0} = 0.5997$

What is the probability that at least one American is left‑handed or at least three Americans are right‑handed?

0.4003 + 0.3271 + 0.5997 = 1.3271

132.71% probability that at least one American is left‑handed or at least three Americans are right‑handed

Answer from: Quest

0/5 is 0, 2/0 is undefined, and 0/0 is indeterminate.

step-by-step explanation:

hope my answer has you!

Answer from: Quest

1) is right

step-by-step explanation:

Can someone helm me with this problem plz and show work

Another question on Mathematics

Mathematics, 21.06.2019 16:50

The table represents a linear function. what is the slope of the function? –6 –4 4 6

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Jack did 3/5 of all problems on his weekend homework before sunday. on sunday he solved 1/3 of what was left and the last 4 problems. how many problems were assigned for the weekend?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

On traditional maps, earth is represented in a flat plane, or by euclidean geometry. however, a globe is a more accurate model that comes from elliptical geometry.how does a globe represent the fact that there are no parallel lines in elliptical geometry? the equator is not parallel to any other latitudinal lines. the north and south poles are never connected by a geodesic. the geodesics connecting the north and south poles never intersect. the geodesics connecting the north and south poles intersect at both of the poles.

Answers: 3

Answer

Mathematics, 21.06.2019 23:00

Can someone me with my math problems i have a bunch. i will give brainliest and lots of pleeeaaasssee

Answers: 2

Answer

You know the right answer?

Arecent harvard study shows that approximately 12% of americans are left‑handed. suppose alex takes...

Questions

Mathematics, 04.12.2020 01:40

The square in the middle has an area of 1 square unit. What is the area of the entire rectangle in square units? Explain your reasoning. A rectangle c...