Miguel buys a large bottle and a small bottle of juice.The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1,024 ml and a standard deviation of 12 ml.The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 504 ml and a standard deviation of 2 ml.If the total amount of juice in the two bottles can be described by a normal model,what's the probability that the total amount of juice in the two bottles is more than 1,554.8 ml?
A)0.014
B)0.011
C)0.018
D)0.986
E)0.982

Question

Quizplus · Accepted Answer

The total amount of juice in the two bottles is the sum of two independent normal random variables. Therefore, the total amount of juice in the two bottles is also a normal random variable with a mean of 1,024 + 504 = 1,528 ml and a standard deviation of sqrt(12^2 + 2^2) = 12.25 ml. The probability that the total amount of juice in the two bottles is more than 1,554.8 ml is P(X > 1,554.8) = 1 - P(X <= 1,554.8) = 1 - 0.986 = 0.014.

Miguel Buys a Large Bottle and a Small Bottle of Juice.The