Help Please

Dec 2019
1
0
Virginia
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 = 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) 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?
 

romsek

MHF Helper
Nov 2013
6,667
3,005
California
$1 - \Phi\left(\dfrac{40-37}{5}\right)$

where $\Phi(x)$ is the CDF of the normal distribution (what you look up in a table or software)


for (b), given the distribution of a single interview given in (a), what is the distribution of the sum of 9 of these?
Use that to evaluate $P[\text{sum of the 9 interview lengths} > 9\cdot 40]$