The amount filled by a certain bottling machine,X,is approximately normally distributed with unknown mean,μ,and standard deviation,σ =1.What is the minimum sample size,n,so that there is a probability of (at least)0.9 that the sample mean will be within 0.2 ounces of the population mean?
A)16
B)28
C)54
D)68
E)125

Question

Quizplus · Accepted Answer

To achieve a 0.9 probability that the sample mean is within 0.2 ounces of the population mean, we use the formula for the sample size in a normal distribution: n = (Z*σ/E)^2. For a 90% confidence level, Z is approximately 1.645. Plugging in the values: n = (1.645*1/0.2)^2 = 67.65, which rounds up to 68.

The Amount Filled by a Certain Bottling Machine,X,is Approximately Normally