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 = 37 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?
a)
This is a normal distribution question with
P(x > 40.0)=?
The z-score at x = 40.0 is,
z = 0.3333
This implies that
P(x > 40.0) = P(z > 0.3333) = 1 - 0.6305460803074295
b)
Sample size (n) = 9
Since we know that
P(x > 40.0)=?
The z-score at x = 40.0 is,
z = 1.0
This implies that
P(x > 40.0) = P(z > 1.0) = 1 - 0.8413447460685429
PS: you have to refer z score table to find the final probabilities.
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