Use the following information for questions:
A bank offers free coffee to its customers. The coffee is brewed each morning in a large coffee urn, and the amount brewed varies slightly. It is independent from day to day, with mean of 125 ounces and standard deviation of 3 ounces. The amount customers drink from day to day is also random, with mean of 100 ounces and standard deviation of 5 ounces, and is independent of the amount brewed.
-If the amount of coffee brewed and the amount of coffee customers drink are both normally distributed, what is the probability that amount of coffee remaining at the end of a day exceeds 40 ounces?
A) 0
B) 0.0051
C) 0.9949
D) 0.4000

Question

Use the following information for questions:
 A bank offers free coffee to its customers. The coffee is brewed each morning in a large coffee urn, and the amount brewed varies slightly. It is independent from day to day, with mean of 125 ounces and standard deviation of 3 ounces. The amount customers drink from day to day is also random, with mean of 100 ounces and standard deviation of 5 ounces, and is independent of the amount brewed.
-If the amount of coffee brewed and the amount of coffee customers drink are both normally distributed, what is the probability that amount of coffee remaining at the end of a day exceeds 40 ounces?
A) 0
B) 0.0051
C) 0.9949
D) 0.4000

Quizplus · Accepted Answer

The amount of coffee remaining is normally distributed with mean 25 ounces (125 - 100) and standard deviation √(3² + 5²) = √34 ounces. To find the probability that the remaining coffee exceeds 40 ounces, calculate the z-score for 40 ounces and use the standard normal distribution table. The z-score is (40 - 25) / √34 ≈ 2.57, and the probability of exceeding this z-score is approximately 0.0051.

Use the Following Information for Questions