SOLUTION: There are 20 people attending an event. A door prize is awarded to attendees if they choose the same number as you randomly pick. Numbers include 1,2,3,4,5. How many prizes shou

Algebra ->  Probability-and-statistics -> SOLUTION: There are 20 people attending an event. A door prize is awarded to attendees if they choose the same number as you randomly pick. Numbers include 1,2,3,4,5. How many prizes shou      Log On


   

Question 523930: There are 20 people attending an event. A door prize is awarded to attendees if they choose the same number as you randomly pick. Numbers include 1,2,3,4,5.
How many prizes should you expect to be won?
How many prizes do you need to be 93% confident you have enough for all winners?
My attempt. I'm pretty sure the number randomly picked would be µ = 3.
Can I say that 1/4 people will pick each of the 5 numbers? So 4 people would choose 3 as their number. Therefore, I would expect 4 people to win.
I am lost on the confident part. We have not gone over that yet.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
How many prizes should you expect to be won? mu=np+=+20+%2A+.2+=+4
.
How many prizes do you need to be 93% confident you have enough for all winners?
sigma=sqrt%28npq%29=sqrt%2820%2A.2%2A.8%29=1.789
z[.93](one tailed)=1.476
%28x-mu%29%2Fsigma=1.476
(x-4)/1.789=1.476 Number of prizes you need = x
x-4=2.64
x=6.64 or 7 prizes you need to be 93% confident.
.
Ed