Question

The times required for a delivery firm to transport a package from one business address to another in the same metropolitan area is normally distributed with a mean of 3.8 hours and a standard deviation of 0.8 hours. Suppose the delivery firm wants to determine the time by which 55% of all deliveries would be made. Which of the following density function diagrams best depicts this problem.

What is the probability a single delivery would take more than 4 hours? What is the z value corresponding to the interval boundary?

Answer 1

Explanation:

Since; the density function diagrams were not included in the question; we will be unable to determine the best which depicts this problem.

However;

Let use X to represent the time required for the delivery.

Then X~N(3.8 ,0.8)

i.e

E(x) = 3.8

s.d(x) = 0.8

NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)

= P(Z > 0.25)

= 1-P(Z < 0.25)

=1 - Φ (0.25)

= 1 - 0.5987 ( from Normal table Φ (0.25) = 0.5987 )

= 0.4013

Thus; the probability a single delivery would take more than 4 hours is 0.4013

What is the z value corresponding to the interval boundary?

The z value is calculated as:

`z = (X- \mu)/(\sigma)`

`z = (4- 3.8)/(0.8)`

z = 0.25