Question

A courier service company has found that their delivery time of parcels two clients is approximately normally distributed with a mean delivery time of 30 minutes and a variance of 25 minutes (squared).

a) what is the probability that a random selected parcel will take more than 26 minutes to deliver?

b) what is the minimum delivery time (minutes) for the 2.5% parcels with the longest time to deliver?

Answer 1

a)

$z=\frac{t-\mu}{\sigma}=\frac{26-30}{\sqrt{25}}=0.80$

$P(t>26)=P(z>0.80)=1-0.78814=0.21186$

b)

For the 2.5% parcels with the longest time to deliver:

$z=Z_{0.975}=1.96$

$1.96=\frac{t-30}{5}$

$t=5\cdot1.96+30=39.8\ min$