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 .18 ounce.

a. Find the probability that a randomly selected carton contains 16.20 to 16.50 ounces of ice cream.

b. What percentage of such cartons contain less than 15.70 ounces of ice cream?
c. Is it possible for a carton to contain less than 15.20 ounces of ice cream? Explain.

Explanation / Answer

Mean = 16 ounces

Standard deviation = 0.18 ounces

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

a) Probability that a randomly selected carton contains 16.20 to 16.50 ounces of ice cream

= P(X < 16.5) - P(X < 16.2)

= P(Z < (16.5 - 16)/0.18) - P(Z < (16.2 - 16)/0.18)

= P(Z < 2.78) - P(Z < 1.11)

= 0.9973 - 0.8665

= 0.1308

b) Probability that a cartons contain less than 15.70 ounces of ice cream = P(X < 15.7)

= P(Z < (15.7 - 16)/0.18)

= P(Z < -1.67)

= 0.0475

4.75% of such cartons contain less than 15.70 ounces of ice cream

c) z = (15.2 - 16)/0.18 = -4.44

P(X < -4.44) = 0.000004

So, it is highly unlikely that a carton will contain less than 15.20 ounces of ice cream

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