Question

the personnel office at a large Electronics firm regularly scheduled 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 equals 34 minutes and standard deviation equals 5 minutes. round your answers to four decimal places
a) what is the probability that a first interview will last 40 minutes or longer?
b) Two first interviews are usually scheduled per day, what is the probability that the average length of time for the two interviews will be 40 minutes or longer?

Answer 1

Solution :

Given that ,

mean = = 34

standard deviation = = 5

a) P(x > 40) = 1 - p( x< 40)  

=1- p P[(x - ) / < (40 - 34) / 5]

=1- P(z < 1.20)

Using z table,

= 1 - 0.8849

= 0.1151

b) n = 2

=   = 34

= / n = 5 / 2 = 3.536

P( > 40) = 1 - P( < 40)

= 1 - P[( - ) / < (40 - 34) / 3.536]

= 1 - P(z < 1.70)

Using z table,    

= 1 - 0.9554

= 0.0446