Suppose 49% of the population has a retirement account. If a random sample of size 896 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?

The probability is  

Step-by-step explanation:

From the question we are told that

  The population proportion is  

  The sample size is  n = 896

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

=>  

=>  

   Generally the the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is mathematically represented as

=>

=>  

=>  

From the z table  the area under the normal curve to the left corresponding to  1.796 and  - 1.796  is  

So

=>