Chocolate bars produced by a certain machine are labeled 8.0 ounces.The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces.If the quality control manager takes a simple random sample of 10 chocolate bars from the production line,what is the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 ounces?
A)0
B)0.00078
C)0.0316
D)0.1587

Question

Quizplus · Accepted Answer

We need to find the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 ounces. We can use the Central Limit Theorem to approximate the distribution of the sample mean as Normal with a mean of 8.1 and a standard deviation of 0.1/sqrt(10) = 0.0316.

Z = (8 - 8.1) / 0.0316 = -3.16

Using a standard Normal distribution table, we can find the probability that Z is less than -3.16 to be 0.00078. Therefore, the probability that the sample mean weight of the 10 sampled chocolate bars will be less than 8.0 ounces is 0.00078.

Chocolate Bars Produced by a Certain Machine Are Labeled 8