Answer to Question #256226 in Statistics and Probability for Sheryl

Question

A machine at Keats Corporation fills 64-ounce detergent jugs. The machine can be adjusted to pour, onaverage, any amount of detergent into these jugs. However, the machine does not pour exactly the sameamount of detergent into each jug; it varies from jug to jug. It is known that the net amount of detergentpoured into each jug has a normal distribution with a standard deviation of .35 ounce. The quality controlinspector wants to adjust the machine such that at least 95% of the jugs have more than 64 ounces ofdetergent.Whatshouldthemeanamountofdetergentpouredbythismachineintothesejugsbe?

Answer 1

Normal distribution with standard deviation s=0.34 ounce

Let X ounce be the amount of detergent filled in the jug.

To find mean corresponding to P(X> 64) = 0.95

Converting this probability in terms of Z from Z-table,

P(Z> -1.645) = 0.95

Let u be the mean

$\frac{(64-u)}{s} = -1.645 \\ u = 64+1.645 \times s \\ u = 64 + 1.645 \times 0.35 \\ u = 64 + 0.57575 \\ u= 64.57575$