Recent census data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125 young adults in this age group was selected. What is the probability that between 14 and 20 of these young adults lived with their parents?

The  probability is    

Step-by-step explanation:

From the question we are told that

   The  proportion that live with their parents is  

   The  sample  size is n =  125

Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

  i.e  

Now the mean is evaluated as

Generally the proportion that are not staying with parents is  

= >    

The standard deviation is mathematically evaluated as

Given the n is large  then we can use normal approximation to evaluate the probability as follows  

Now applying continuity correction

Generally  

So  for the z -  table  

the two may have that, even a breakdown is probably offered