Mathematics, 08.11.2019 22:31 darlaaa

An interviewer is given a list of people she can interview. if the interviewer needs to interview 5 people, and if each person (independently) agrees to be interviewed with probability 2/3, what is the probability that her list of people will enable her to obtain her necessary number of interviews if the list consists of (a) 5 people and (b) 8 people? for part (b), what is the probability that the interviewer will speak to exactly (c) 6 people and (d) 7 people on the list?

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Answer from: BEEFYTACO

a) 0.1317

b) 0.7413

c) 0.2731

d) 0.1561

Step-by-step explanation:

Let's start defining the random variable.

X : ''The number of people that she interviews''

X ~ Bi (n,p)

This means, X can be modeled as a Binomial random variable where p is the success probability and n is the number of independent Bernoulli experiments that take place. In this case, n is the number of interviews that she makes.

The probability function for X is :

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

Where nCx is the combinatorial number defines as :

$nCx=\frac{n!}{x!(n-x)!}$

For a)

We are looking for the probability of she interviews 5 people over 5 she interviews ⇒

$P(X=5)=(5C5)(\frac{2}{3})^{5}(\frac{1}{3})^{0}=\frac{32}{243}=0.1317$

b) In this part , we are looking for P(X ≥ 5) when n = 8 (Number of people she interviews)

$P(X\geq 5)= P(X=5)+P(X=6)+P(X=7)+P(X=8)$

$P(X\geq 5)=(8C5)(\frac{2}{3})^{5}(\frac{1}{3})^{3}+(8C6)(\frac{2}{3})^{6}(\frac{1}{3})^{2}+(8C7)(\frac{2}{3})^{7}(\frac{1}{3})^{1}+(8C8)(\frac{2}{3})^{8}(\frac{1}{3})^{0}=0.7413$

c) Interview 6 people of 8 :

$P(X=6)=(8C6)(\frac{2}{3})^{6}(\frac{1}{3})^{2}=0.2731$

d) Interview 7 people of 8 :

$P(X=7)=(8C7)(\frac{2}{3})^{7}(\frac{1}{3})^{1}=0.1561$

Answer from: Quest

answer: rolling a number cube and flipping a coin.

step-by-step explanation:

Will mark brainliest if you answer a few easy questions! asap! !

Answer from: Quest

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.

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