Question

In: Statistics and Probability

QUESTION 5 [4] A courier service company has found that their delivery time of parcels to...

QUESTION 5 [4]

A courier service company has found that their delivery time of parcels to 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 randomly selected parcel will take between 26 and 42 minutes to deliver? (2)

b) What is the maximum delivery time (minutes) for the 2.5% of parcels with the shortest time to deliver? (2)

Expert Solution

Solution: We are given:

a) We are required to find:

Using the z-score formula, we have:

Using the standard normal table, we have:

Therefore, the probability that a randomly selected parcel will take between 26 and 42 minutes to deliver is 0.7799

b) We have to first find the z-value corresponding to area = 0.025. Using the standard normal table, we have:

Now using the z-score formula, we have:

Therefore, the maximum delivery time (minutes) for the 2.5% of parcels with the shortest time to deliver is 20.2 minutes

orchestra answered 1 year ago

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