A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. Actual quantities dispensed vary,and the amounts are normally distributed with a standard deviation of 0.015 liters. What is the probability a container will have less than 2 liters?
A)0.0918
B)0.3413
C)0.1926
D)0.8741

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the normal distribution formula:

Z = (X - μ) / σ

where X = 2 liters, μ = 2.02 liters, and σ = 0.015 liters.

So, Z = (2 - 2.02) / 0.015 = -1.33

Using a standard normal table or calculator, we can find the probability that Z is less than -1.33, which is 0.0918.

Therefore, the probability that a container will have less than 2 liters is 0.0918, or approximately 9.18%. The closest answer choice is A.

A Cola-Dispensing Machine Is Set to Dispense a Mean of 2.02