a) Determine the expected number of convicted drivers out of 15 selected drivers

Tabansi

Tabansi

Answered question

2021-09-20

a) Determine the expected number of convicted drivers out of 15 selected drivers who were arrested for DWI.
b) Determine the probability that exactly 11 out of the 15 independent selected drivers are convicted.
c) Determine the probability that 11 or fewer out of the 15 independent selected drivers are convicted for DWI.

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-09-21Added 120 answers

a) The conviction rate of DWI in Mexico is 70% for the drivers who were arrested. 
The following are the presumptions for determining whether the binomial model fits the data:
n trials, all of the same size.
There should only be two possible results for each trial.
The probability of success is equal for all trials. 
The trials are independent. 
Requirement check: 
There are 15 drivers who were arrested for DWI n=15
There are only two possible outcomes that can occur "Convected" and "Not Convicted". 
For all the drivers who were stopped for DWI, the likelihood of conviction is the same.
For all drivers, the likelihood of conviction is the same.
Therefore, the given experiment can make use of the binomial model.
The expected number of drivers who were convicted is calculated below. 
E(X)=np 
=15×0.7 
=10.5 
This shows that it is possible to expect 10 or 11 drivers to be convicted if 15 independently selected drivers were arrested for DWI. 
b) The conviction rate of DWI in Mexico is 70% for the drivers who were arrested. 
It is determined in part(a) that binomial model can be used for the given experiment. 
Use Excel to calculate the point wise binomial probability. The steps for calculating the required probability using Excel spreadsheet are given below. 
Click fx
Choose BINOM.DIST. Click Ok. 
Enter Number_s:11, Trials 1 5, Probability_s: 0.70 and Cumulative: False 
Click Ok. 
Excel windows shows that the required probability is 0.219. 
Therefore, the probability that 11 out of the 15 independent selected drivers are convicted is 0.219. 
c) The conviction rate of DWI in Mexico is 70% for the drivers who were arrested. 
Use Excel to calculate the cumulative binomial probability. The steps for calculating the required probability are given below. 
Click fx
Choose BINOM.DIST. Click Ok. 
Enter Number_s:11, Trials 1 5, Probability_s: 0.70 and Cumulative: TRUE(this is for the probability of 7 or fewer). 
Click Ok. 
Excel windows shows that the required probability is 0.703. 
Therefore, the probability that 11 out of the 15 independent selected drivers are convicted is 0.703.

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