Mathematics, 25.11.2019 19:31 blake4033

Trainees must complete a specific task in less than 2 minutes. consider the probability density function below for the time it takes a trainee to complete the task. f(x) = 0.85 - 0.35x0 < x < 2a) what is the probability a trainee will complete the task in less than 1.31 minutes? give your answer to four decimal places. b) what is the probability that a trainee will complete the task in more than 1.31 minutes? give your answer to four decimal places. c) what is the probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task? give your answer to four decimal places. d) what is the expected time it will take a trainee to complete the task? give your answer to four decimal places. e) if x represents the time it takes to complete the task, what is e(x2)? give your answer to four decimal places. f) if x represents the time it takes to complete the task, what is var(x)? give your answer to four decimal places.

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Answer from: ummitsjustjae

a) 0.8132 or 81.32%

b) 0.1868 or 18.68%

c) 0.6116 or 61.16%

d) 0.7667 minutes

e) 0.8667 minutes

f) 0.1 minutes

Step-by-step explanation:

If f(x) = 0.85-0.35x (0<x<2) is the PDF and X is the random variable that measures the time it takes for a trainee to complete the task, the probability a trainee will complete the task in less than 1.31 minutes is P(X<1.31)

$\large P(X$

The probability that a trainee will complete the task in more than 1.31 minutes is

P(X>1.31) = 1 - P(X<1.31) = 1 - 0.8132 = 0.1868

The probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task is P(0.25<X<1.31)

$\large P(0.25$

the expected time it will take a trainee to complete the task

is E(X)

$\large E(X)=\int_{0}^{2}xf(x)dx=\int_{0}^{2}x(0.85-0.35x)dx=0.85\int_{0}^{2}xdx-0.35\int_{0}^{2}x^2dx=\\\\=0.85*\frac{2^2}{2}-0.35*\frac{2^3}{3}=0.7667\;minutes$

$\large E(X^2)=\int_{0}^{2}x^2f(x)dx=\int_{0}^{2}x^2(0.85-0.35x)dx=0.85\int_{0}^{2}x^2dx-0.35\int_{0}^{2}x^3dx=\\\\=0.85*\frac{2^3}{3}-0.35*\frac{2^4}{4}=0.8667$

$\large Var(X)=E(X^2)-(E(X))^2=0.8667-0.7667=0.1000$

Answer from: Quest

answer: segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality. in the case of brown v. board of education, that standard was challenged and defeated. segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to education. this was being violated by states whose laws supported the segregation of schools. section 1 of the 14th amendment reads as follows:

all persons born or naturalized in the united states and subject to the jurisdiction thereof, are citizens of the united states and of the state wherein they reside. no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united states; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Answer from: Quest

nada

step-by-step explanation:

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