Question

A company is interviewing potential employees in order to fill some open positions. The probability that the candidate being interviewed has the necessary qualifications is 0.3. a) What is the probability that, o exactly 6 employees out of 50 applicants are hired? o at most 15 employees out of 50 applicants are hired? b) If the company stops the interviews as soon as the open positions are filled, what is the probability that, o the interview finishes before the 6th applicant, given that there is a single open position? o the interview finishes before the 8th applicant, given that there are three open positions? c) If the company stops the interviews as soon as the single open position is filled, what is the expected number of interviews the company makes?

          A company is interviewing potential employees in order to fill
some open positions. The probability that the candidate being
interviewed has the necessary qualifications is 0.3. a) What is the
probability that, o exactly 6 employees out of 50 applicants are
hired? o at most 15 employees out of 50 applicants are hired? b) If
the company stops the interviews as soon as the open positions are
filled, what is the probability that, o the interview finishes
before the 6th applicant, given that there is a single open
position? o the interview finishes before the 8th applicant, given
that there are three open positions? c) If the company stops the
interviews as soon as the single open position is filled, what is
the expected number of interviews the company makes?

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Added by Joyce M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Rosina Dapaah

12/18/2021

Step 1

Since we are dealing with a fixed number of trials (50 applicants), each with two possible outcomes (qualified or not qualified), and a constant probability of success (0.3), this is a binomial distribution problem. Show more…

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A company is interviewing potential employees in order to fill some open positions. The probability that the candidate being interviewed has the necessary qualifications is 0.3. a) What is the probability that, o exactly 6 employees out of 50 applicants are hired? o at most 15 employees out of 50 applicants are hired? b) If the company stops the interviews as soon as the open positions are filled, what is the probability that, o the interview finishes before the 6th applicant, given that there is a single open position? o the interview finishes before the 8th applicant, given that there are three open positions? c) If the company stops the interviews as soon as the single open position is filled, what is the expected number of interviews the company makes?

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Transcript

00:01 So we know that the binomial distribution has a p and a 4.

00:09 And choose x.

00:11 Then you have p to the power x, then 1 minus p to the power n minus x.

00:18 So based on our data, we have p is equal to 0 .3.

00:23 We have n is equal to 50.

00:26 So to find the probability of x is equal to 6, then we are going to get n, which is 50, choose 6.

00:37 Then we have our probability of 0 .3 to the power of 6 we have 1 minus 0 .3 to the power 50 minus 6 so from here we get 0 .017 but the probability of x is equal to 6.

01:08 Similarly we are given you are actually find the probability of x greater than or equal to 15.

01:16 So this will be equal to 50 choose 15.

01:23 You have 0 .3 to the power 15 times 0 .7 to the power 50 minus 15.

01:35 So this will be equal to 50 choose 15 into 0 .3 to the power 15, 0 .7 to the power 45.

01:47 Then we get the probability of x -weta or equal to 15 to be 0 .3.

01:52 5, 6, 91.

01:55 So for our b part, so given that the probability of x is less than 6, we know this will be equal to the probability of x equal to 1, plus the probability of x equal to 2, up to the probability of x equal to 5.

02:30 So we are going to get, for the probability of x equal to 1, we are going to get 0 .3 are going to get 1 minus 0 .3 times 0 .3 plus i'm going to get 1 minus 0 .3 squared times 0 .3 plus 1 minus 0 .3, 2 2 .3, 1 minus 0 .3, cube, 2 .3 plus 1 minus 0 .3, 2 .4.

03:16 Times 0 .3...

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