SOLUTION: The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length

Question 1079527: The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 32 minutes and standard deviation σ = 9 minutes. (Round your answers to four decimal places.)
(a) What is the probability that a first interview will last 40 minutes or longer?

(b) Nine first interviews are usually scheduled per day. What is the probability that the average length of time for the nine interviews will be 40 minutes or longer?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 32 minutes and standard deviation σ = 9 minutes. (Round your answers to four decimal places.)
(a) What is the probability that a first interview will last 40 minutes or longer?
z(40) = (40-32)/9 = 8/9
P(x >= 40) = P(z >= 8/9) = normalcdf(8/9,100) = 0.1870
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(b) Nine first interviews are usually scheduled per day. What is the probability that the average length of time for the nine interviews will be 40 minutes or longer?
z(40) = (40-32)/(9/sqrt(9)) = 8/3
P(x-bar >= 40) = P(z >= 8/3) = normalcdf(8/3,100) = 0.0038
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cheers,
Stan H.
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