Part II. (9 points) Consider X to be a random variable that is modeled by a pois
ID: 2921225 • Letter: P
Question
Part II. (9 points) Consider X to be a random variable that is modeled by a poisson distribution, X, represents the number of cars per hour at an automatic carwash. For a popular carwash the average number of cars per hour is 8.
Answer the following questions:
a. (2 points) For any hour, what is the probability 12 cars are washed at the carwash?
b. (2 points) For any hour, what is the probability the number of cars is 4 or more?
c. (3 points) Go to the Statistics Interactives tab in the week 0 module. Select interactive 1 on the left side of the page. Choose the Poisson distribution. Put in the parameter value and x = 12.
1. What is the shape of the probability mass function?
2. What is the probability X is 12 according to the software? Is this the same as what you got in part a?
3. Based on the graph of the probability mass function, what is the most likely number of cars at the carwash (most frequent)?
d. (2 points) Suppose the carwash is open from 7AM to 10PM (15 hours a day), how much can the carwash expect to earn a day if they get $10 per carwash?
Explanation / Answer
here average number of cars per hour is = 8 =
a) probability 12 cars are washed at the carwash =P(X=12) =e-x/x! =0.0481
b)probability the number of cars is 4 or more =P(X>=4)=1-P(X<=3) =1- x=33 e-x/x! =1-0.0424 =0.9576
c) 1)shape of the probability mass function ---right skewed
2) it is same
3) most likely numeber is 7 or 8 as they both have equal probability
d) expected number to come in 15 hours =15*8 =120
therefore expected earning =120*10=$1200