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 1018 ml and a standard deviation of 9 ml.The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 506 ml and a standard deviation of 3 ml.Let the random variable T represent the total amount of juice in the two bottles.Suppose that you use a Normal model to determine the probability that the total amount of juice,T,in the two bottles is more than 1543.0 ml.Which of the following assumptions are needed to find the probability in this way? A: The amount of juice in the large bottle is independent of the amount of juice in the small bottle.
B: The amount of juice in each bottle follows a Normal model.
C: The amount of juice in the large bottle is greater than the amount of juice in the small bottle.
A)A and B
B)B only
C)A,B,and C
D)A only
E)No assumptions are needed.

Question

Quizplus · Accepted Answer

To calculate the probability that the total amount of juice exceeds a certain value using a Normal model, it is necessary to assume that the amounts in the large and small bottles are independent (A) and that each follows a Normal distribution (B). Independence is required to correctly aggregate the means and variances, and the Normal distribution assumption allows for the use of Normal probability models. Assumption C is not required for the calculation and does not affect the statistical model.

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