At Jen and Perry Ice Cream Company, the machine that fills 1-pound cartons of To

Question

At Jen and Perry Ice Cream Company, the machine that fills 1-pound cartons of Top Flavor ice cream is set to dispense 16 ounces of ice cream into every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in all such cartons have a normal distribution with a mean of 16 ounces and a standard deviation of 0.32 ounces. What percentage of such cartons contain less than 15.885 ounces of ice cream? Round your answer to two decimal places. %

Explanation / Answer

Mean = 16 ounces

Standard deviation = 0.32 ounces

P(X<X0) = P(Z<(X0 - mean)/standard deviation)

P(X<15.885) = P(Z<(15.885 - 16)/0.32)

= P(Z < -0.36)

From standard normal distribution table,  P(Z < -0.36) = 0.3594

Percentage such cartons contain less than 15.885 ounces of ice cream = 35.94%

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