At Jen and Perry Ice Cream Company, a machine fills 1-pound cartons of Top Flavor ice cream. The machine can be set to dispense, on average, any amount of ice cream into these cartons. However, the...

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At Jen and Perry Ice Cream Company, a machine fills 1-pound cartons of Top Flavor ice cream. The machine can be set to dispense, on average, any amount of ice cream into these cartons. However, the machine does not put exactly the same amount of ice cream into each carton; it varies from carton to carton. It is known that the amount of ice cream put into each such carton has a normal distribution with a standard deviation of .18 ounce. The quality control inspector wants to set the machine such that at least 90% of the cartons have more than 16 ounces of ice cream. What should be the mean amount of ice cream put into these cartons by this machine?




Answered Same DayDec 25, 2021

Answer To: At Jen and Perry Ice Cream Company, a machine fills 1-pound cartons of Top Flavor ice cream. The...

David answered on Dec 25 2021
126 Votes
Find µ for: P (X > 16) = 90%
Normal Distribution
σ = 0.18
P (X > x0) = 0.9 ⇒ P (X < x0) = 0.1
P
(
X − µ
σ
<
x0 − µ
σ
)
= 0.1
⇒ P
(
Z <
x0 − µ
σ
)
= 0.1
⇒ x0 − µ
σ
= invNorm(0.1)
⇒ µ = x0 − σ × invNorm(0.1)
Use z-table to get invNorm(0.1) = −1.282
⇒ µ = 16− 0.18× (−1.282) =...
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