Question

A machine used to fill cereal boxes dispenses, on the average, μ ounces per box. The manufacturer wants the actual ounces dispensed Y to be within 1.1 ounce of μ at least 75% of the time. What is the largest value of σ, the standard deviation of Y, that can be tolerated if the manufacturer's objectives are to be met?

Answer 1

Answer: 1/2

Step-by-step explanation:

First step: we will use Tchebyscheff's theorem. The theorem can help us to explain random variables with finite variance as well as mean.

P (|Y-u| < or equals to 1) | > or equals to 0.75

= 1 - 1/2

Therefore, w= 2

Step 2: we use Tchebyscheff's inequality, which is:

= -2¶ + u < y < 2¶ + u

Therefore, we have; --2¶ + u

= 1 + u

1= K¶

¶ = 1/2.

Please take note that ¶ is represented as sigma symbol.

Since I can't get the symbol here with me. Also the u repres represent 'micro' symbol