Mathematics, 01.07.2021 18:00 SakChan8367

According to a Gallup poll, 60% of American adults prefer saving over spending. In a random sample of 10 American adults, what is the probability that more than 3 adults in the sample prefer saving over spending

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Answer from: BELLE6284

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they prefer saving over spending, or they do not. The answers for each adult are independent, 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.

According to a Gallup poll, 60% of American adults prefer saving over spending.

This means that p = 0.6

Sample of 10 American adults

This means that n = 10

What is the probability that more than 3 adults in the sample prefer saving over spending?

This is:

$P(X 3) = 1 - P(X \leq 3)$

In which

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{10,0}.(0.6)^{0}.(0.4)^{10} = 0.0001$

$P(X = 1) = C_{10,1}.(0.6)^{1}.(0.4)^{9} = 0.0016$

$P(X = 2) = C_{10,2}.(0.6)^{2}.(0.4)^{8} = 0.0106$

$P(X = 3) = C_{10,3}.(0.6)^{3}.(0.4)^{7} = 0.0425$

Then

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0001 + 0.0016 + 0.0106 + 0.0425 = 0.0548$

$P(X 3) = 1 - P(X \leq 3) = 1 - 0.0548 = 0.9452$

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

rauschg · hand

know the answer? add it here!

step-by-step explanation:

Answer from: Quest

6e14 is the answer.

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According to a Gallup poll, 60% of American adults prefer saving over spending. In a random sample o...