A population has a mean of 200 and a standard deviation of 50. Suppose a random sample of 100 people is selected from this population. What is the probability that the sample mean will be within /- 5 of the population mean

Complete Question

A population has a mean of 200 and a standard deviation of 50. Suppose a random sample of 100 people is selected from this population. What is the probability that the sample mean will be within of the population mean

The value is  

Step-by-step explanation:

From the question we are told that  

   The mean is

    The population standard deviation is  

    The sample size is  

Generally the standard error of sample mean is mathematically represented as

=>      

=>    

Generally the limits of    within  the population mean is mathematically represented as

=>  

=>  

and

=>

=>

Generally the probability that the sample mean will be within of the population mean is mathematically represented as

=>    

=>    

=>    

Generally from the  z -table  the probability of  (Z <  1) and  (Z<-1 )  is

and  

So