Question

Imagine getting a ride with Uber is a two-step process. First, you request the ride. It takes an average of 3 minutes to get that request posted and answered, with a standard deviation of 0.85 minutes. Then it takes an average of 6 minutes for your Uber driver to arrive, with a standard deviation of 2 minutes. Both parts are Normally distributed.

(13) What are the mean and standard deviation of the total time it takes from placing the order to being picked up?

            Mean = ______ minutes

            SD = ______ minutes

(14) What is the probability you will wait no more than 5 minutes for your ride?

Answer 1

(13)

Let A be the Event: Request the ride

B be the Event: Uber driver to arrive

Given:

= 0.85

= 2

By Theorem, X = A + B is Normal Distribution with mean :

and

Standard Deviation:

So,

Answer is:

Mean = 9 minutes

SD = 2.1731 minutes

(14)

To find P(X5):

Z = (5 - 9)/2.1731

= - 1.8407

By Technology, Cumulative Area Under Standard Normal Curve = 0.0328

So,

P(X5):= 0.0328

So,

Answer is:

0.0328