SOLUTION: I have worked this problem before and got it wrong and so I'm trying to fix it to get second chance credit but I just dont understand it. Can someone please help? Let X[cm] be t

Algebra ->  Probability-and-statistics -> SOLUTION: I have worked this problem before and got it wrong and so I'm trying to fix it to get second chance credit but I just dont understand it. Can someone please help? Let X[cm] be t      Log On


   

Question 364992: I have worked this problem before and got it wrong and so I'm trying to fix it to get second chance credit but I just dont understand it. Can someone please help?
Let X[cm] be the diameter of bolts in a production. Assume that X has the density f(x)=k(x-0.9)(1.1-x) if 0.9< x <1.1 and 0 otherwise. Determine k. graph f(x), and the mean and variance.
I dont know if there is any way to put graphs on here but if not can you please try and help as much as possible. I would so appreciate it.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The integral of the density function from x=0.9 to x=1.1 must equal 1.
int%28k%28x-0.9%29%281.1-x%29%2Cdx%2C0.9%2C1.1%29=1
k%2Aint%28%28-x%5E2%2B2x-%2899%2F100%29%29%2Cdx%2C0.9%2C1.1%29=1


-602%2F3000%2B1200%2F3000-594%2F3000=1%2Fk
1%2Fk=4%2F3000
highlight%28k=750%29
.
.
graph%28300%2C300%2C0.9%2C1.1%2C-1%2C8%2C750%28x-0.9%29%281.1-x%29%29
.
.
The left endpoint is x=0.9, the right endpoint is x=1.1.
The peak of 7.5 occurs when x=1.
.
.
Now that you have k you can solve for the mean and the variance.


highlight%28mu=1%29
.
.
.


V%2Fk=8%2F3000000
highlight%28V=1%2F500%29