Suppose 52% of the population has a college degree. If a random sample of size 563563 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5%5%? Round your answer to four decimal places.

The value is  

Step-by-step explanation:

From the question we are told that

    The population proportion is  

     The sample size is  n  =  563      

Generally the population mean of the sampling distribution is mathematically  represented as

Generally the standard deviation of the sampling distribution is mathematically  evaluated as

=>      

=>      

Generally the  probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

  Here   is the sample proportion  of persons with a college degree.

So

Here  

=>

=>

=>  

From the z-table  the probability of  (Z <  2.37 ) and  (Z < -2.37 ) is

and

So

=>

=>

=>