The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the probability of obtaining a sample mean within 0.04 ounces of the population mean? a. 0.9545
b. 0.0363
c. 0.3085
d. 0.5000

The probability of obtaining a sample mean is "0.9545".

According to the question,

Mean,

Standard deviation,

Random sample,

By Central limit theorem,

→

Now,

→

Thus the above response i.e., "option a" is appropriate.

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The standard error of the mean is 0.02

Step-by-step explanation:

Here, we want to calculate the standard error of the mean.

Mathematically;

standard error of mean = SD/ √n

where SD is the standard deviation and n is the number of samples

From the question, SD = 0.22 and n = 121

Inserting this into the equation

Standard error of the mean = 0.22/√121

= 0.22/11 = 0.02