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

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Question 871685: 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 a mean of 35 and standard deviation of 7 minutes
a. what is the probability that the mean length of time for a group of nine interviews is greater than 40 minutes
b. what is the probability that the mean length of time for a group of nine interviews is between 32 and 37 minutes
c. what is the mean length of time for a group of nine interviews that cuts off the bottom 10% of the distributiion
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

mean of 35 and standard deviation of 7 minutes

Sample size 9, s = 7/sqrt(9) = 7/3

a)  P(x > 40), z = 5/(7/3) = 15/7 = 2.1429,  P(z > 2.1429) = .0161  0r 1.61%

b)  P(32 ≤ x ≤ 37) = normalcdf(32,37,35, 7/3)

c) invNorm(.10) = -1.282

-1.282 = (X - 35)/(7/3)

(2.333)(-1.282) + 35 = X