What is the probability that a random sample of 400 U. S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p)?

Complete Question

The proportion of adult women in the United States is 51% (p=0.51).What is the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p)?

The probability is    or  

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  400

    The population proportion is  p = 0.51

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

=>      

=>      

Generally the lower limit for the range of the population proportion within 0.03 is

=>

=>

Generally the  upper  limit for the range of the population proportion within 0.03 is

=>

=>

Generally the  probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p) is mathematically represented as

=>  

=>  

=>  

From the z table  the area under the normal curve to the left corresponding to  1.2 and  -1.2  is

and  

So

=>  

the image of (6, 9) under a dilation is (4, 6). the scale factor is