A paint manufacturer has a daily output X is normally distributed with an average of 450 000 L and a standard deviation of 45 000 L. The states conduit company made available an incentive for the production department. If the daily production is greater than the 90th percentile of the distribution, the department receives a premium. Determine the height of the production conduit in which the payment of premium.
Can someone explain to me how to solve this plz?
+118723 I am a bit rusty on questions like this but this is what I think
A paint manufacturer has a daily output X is normally distributed with an average of 450 000 L and a standard deviation of 45 000 L. The states conduit company made available an incentive for the production department. If the daily production is greater than the 90th percentile of the distribution, the department receives a premium. Determine the height of the production conduit in which the payment of premium.
I used this site
http://davidmlane.com/hyperstat/z_table.html
and put in that I wanted 90% below..... it gave me a z score of 1.282
You may have needed to work this out from the body of a z score table
Now you have
z=1.282
mean=450,000L
SD= 45000L
now you just need to use the formula to get the x score
\(1.282=\frac{x-450000}{45000}\\ 1.282*45000=x-450000\\ 57690=x-450000\\ 57690+450000=x\\ x=507690\\\)
So I think the premium is paid if the production is over 507 690 L
