
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 11th, 2018, 03:43 PM  #1 
Member Joined: Feb 2018 From: Canada Posts: 34 Thanks: 2 
For a shirt ironing service at the dry cleaners, they charge a base price of \$3 plus an additional \$1.50 per shirt to be ironed. Suppose the number of shirts customers at the dry cleaners require to be ironed follows a Poisson distribution with mean 4.5. What is the probability a random customer in the store will use the dry cleaning service and spend no more than \$10 on the dry cleaning services? I am having a problem with this question, for mean 4.5 shirts, I think the price would be \$3 + \$1.5*3.5 = \$8.25. If X be the number of shirts customers at the dry cleaners require to be ironed, then Y be an amount of money customer have to pay for the services. Then Y = \$3 + \$1.5*(X  1). Since X follows a Poisson distribution with mean 4.5, Y would follow a Poisson distribution with $\lambda$ = 8.25. Am I right? Last edited by skipjack; March 20th, 2018 at 04:04 AM. 
March 12th, 2018, 06:21 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087 
I would convert things the other way. Spending no more than \$10 is the same as having no more than 4 shirts ironed. So we evaluate $P[X \leq 4]$, where $X$ is a Poisson distributed rv with $\lambda = 4.5$ $P[X \leq 4] \approx 0.5321$ Last edited by romsek; March 12th, 2018 at 07:07 PM. 
March 12th, 2018, 10:51 PM  #3  
Member Joined: Feb 2018 From: Canada Posts: 34 Thanks: 2  Quote:
How would you come up with 4 shirts. If X is the number of shirts customers at the dry cleaners require to be ironed then Y be a amount of money customer have to pay for the services. So, $Y=3+1.5*(X1)$ $10=3+1.5*(X1) \text{ then } X \approx 5$ $P[X \leq 5]$, where $X$ is a Poisson distributed rv with $\lambda = 4.5$ $P[X \leq 5] \approx 0.7029304$ Last edited by Shanonhaliwell; March 12th, 2018 at 10:57 PM.  
March 12th, 2018, 11:19 PM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,091 Thanks: 1087  Quote:
5 shirts cost \$3 + 5(\$1.5) = \$10.5 > 10 oh, are you saying the base \$3 gets you 1 shirt ironed? In that case you're right. You can get 5 shirts ironed < \$10 $P[X \leq 5] \approx 0.70293$  
March 12th, 2018, 11:43 PM  #5  
Member Joined: Feb 2018 From: Canada Posts: 34 Thanks: 2  Quote:
Thanks. Last edited by Shanonhaliwell; March 12th, 2018 at 11:52 PM.  
March 16th, 2018, 07:53 AM  #6 
Newbie Joined: Mar 2018 From: Canada Posts: 1 Thanks: 0 
Can someone post the every step of this question please ? Thanks


Tags 
distribution, poisson, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Poisson Distribution  UncleFester  Algebra  4  January 19th, 2016 03:27 AM 
Negative exponential distribution to the poisson distribution  alan02011114  Advanced Statistics  0  April 21st, 2015 10:03 AM 
Can anybody decode a Poisson distribution problem?!!!!  Yoha  Advanced Statistics  6  March 1st, 2012 07:46 PM 
Poisson distribution and binomial distribution questions  latkan  Advanced Statistics  1  May 11th, 2009 05:49 AM 