Expected value and Standard deviation

#1
I have a problem about expected value that I was wondering if I did right:

Walmart is hosting a sale. Customers choose a random ticket that is takes 5%, 15%, or 25% off their total purchase. Ten percent of the tickets are labeled 25%, Twenty percent are labeled 15%, and the remaining are labeled 5%. What is the expected actual sale for a customer wishing to purchase $100 worth of merchandise?
Here's my work and answer: $75(.10) + $85(.20) + $95(.70) = $118.8



There's one more problem I need help with
The weight for a population of animal species follows a normal distribution. It is determined that 10% weights exceed 12.513, and 1% of the weights exceed 12.930. What are the mean and standard deviation of this population of battery voltages?
This one I'm not sure about. I tried looking at the normal curve and appying the 68-95-99.7, but that didn't work cause it wasn't even. I think I'm supposed to divide the differences or something?

Any help is appreciated :]
 

Dragan

Super Moderator
#2
What are the mean and standard deviation of this population of battery voltages?

Any help is appreciated :]

I would say that the mean is approximately 12 and the standard deviation is approximately 0.4


I determined this by looking at the problem as if I had two equations with two unknowns. Specifically,


1.28 = (12.51 - Mu) / Sigma

and

2.33 = (12.93 - Mu)/ Sigma.

Simultaneously solving these equations gives the result that I suggested above.


Note: 1.28 and 2.33 are Z scores from the unit normal density associated with .1 and .01.

Hope this helps.
 
#3
Ok, I understand now. I don't know why I didn't remember to use that formula earlier. I get why you used that, but how did you solve for the values when there were two missing variables? Thanks a lot for the help.
 

Mean Joe

TS Contributor
#5
I have a problem about expected value that I was wondering if I did right:

Walmart is hosting a sale. Customers choose a random ticket that is takes 5%, 15%, or 25% off their total purchase. Ten percent of the tickets are labeled 25%, Twenty percent are labeled 15%, and the remaining are labeled 5%. What is the expected actual sale for a customer wishing to purchase $100 worth of merchandise?
Here's my work and answer: $75(.10) + $85(.20) + $95(.70) = $118.8
Your reasoning is spot on, but the final answer is wrong; it should be $91 (I think). It should definitely be less than $100.
 
#6
Yeah, I tried calculating it again and got $91 as an answer instead. But everything was correct? I used the Sumof(Xi*Pi) formula from my book.
Thanks a lot!