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?

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 :

Where nCx is the combinatorial number defines as :

For a)

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

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

c)  Interview 6 people of 8 :

d) Interview 7 people of 8 :

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1