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 0.05 ounces of the population mean?

The probability is

Step-by-step explanation:

From the question we are told that

   The population mean is  

    The standard deviation is  

    The sample size is  n =  121

Generally the standard error of mean is mathematically represented as

=>      

=>      

The upper limit of the interval within which the sample is consider be found in is

=>      

=>      

The lower limit of the interval within which the sample is consider be found in is

=>      

=>    

Generally the probability of obtaining a sample mean within 0.05 ounces of the population mean is mathematically represented as

=>  

=>  

=>  

From the z table  the area under the normal curve to the left corresponding to  2.5 and  -2.5  is

=>    

So

=>  

m

step-by-step explanation: