The amount of cereal dispensed into 16ounce boxes of Captain

The amount of cereal dispensed into \"16-ounce\" boxes of Captain Crisp cereal was normally distributed with mean 16.12 ounces and standard deviation 0.20 ounces.

Suppose that the machine can be adjusted to change the mean while the standard deviation remains at 0.20 ounces. What must the mean be so that only 20% of all the boxes are \"underfilled\"?

Solution

let x be the mean for which only 20% boxes ara under filled

P(x>16) = 20%

P(Z> 16-mean/0.2) = 20%

=> 16-mean/0.2 = 1 - invnorm(20%)

=>

16-mean/0.2 = 1 - (-0.842)

=>

mean = 15.6316