Question

UPS carefully plans routes for its trucks on a daily basis and tracks every driver’s stops electronically using sophisticated GPS technology. UPS drivers are allowed three minutes per hour of lag time in delivery (e.g., route construction, traffic accident, rain, snow). Construct the appropriate distribution in Excel and create a table finding probabilities for all range of possibilities of delivery time lags (start the distribution at 0 and create and endpoint of 15).

1. What is the probability that the lag time is 0 minutes per hour in delivery; lag time is exactly 3 minutes per hour in delivery?

Answer 1

Define

X: lag time per hour in delivery ( in minutes)

we are to find the distribution of X

it is given that : start the distribution at 0 and create and endpoint of 15

evidently X ~ Binomail (n,p)

where n= number of trials (here lag time in minutes per hour)= 15

p= probability of lag time in each trial( i.e. probability of lag time(in minutes) in each hour)

it is said that UPS drivers are allowed three minutes per hour of lag time in delivery

i.e.on an average lag time per hour is 3 minutes

which means E(X)=3

we know if X~Binomial(n,p)

E(X)=np

np=3

implies p=3/n=3/15=0.2

(since UPS drivers are allowed three minutes per hour of lag time in delivery)

the probability mass function (pmf) of X is given by

where n=15,p=0.2

using this pmf we calculate the  probabilities for all range of possibilities of delivery time lags in Excel.

I am providing the screenshot of Excel output here :

1. The probability that the lag time is 0 minutes per hour in delivery

=P(X=0)

=3.518437e-02=0.0352

The probability that the lag time is exactly 3 minutes per hour in delivery

=P(X=3)=2.501389e-01= 0.25

[ we can cross check the Excel output of calculated values of probabilities using scientific calculator also .

for example :

to find P(X=0)

=0.352

]

Dear student hope I am able to give you clear explanation. If you like my answer please rate it. Thank you !!