Question 5 The proportion of homes in Tennessee owned by investors rather than homeowners is $26 \%$. Consider a sampling distribution where $n=150$. \[ n p= \] \[ n(1-p)= \] Can a normal distribution approximation be used for the sampling distribution of sample proportions? Yes, a normal distribution approximation can be used No, a normal distribution approximation can't be used Submit
Solution
Step 1 ：The proportion of homes owned by investors is given as 26%, which is the value of p. The sample size n is given as 150.
Step 2 ：The conditions for using a normal distribution approximation for the sampling distribution of sample proportions are that np and n(1-p) are both greater than or equal to 5.
Step 3 ：So, we need to calculate np and n(1-p) and check if they are both greater than or equal to 5.
Step 4 ：Let's calculate these values: n = 150, p = 0.26, np = 39.0, n1_p = 111.0
Step 5 ：The calculated values of np and n(1-p) are 39.0 and 111.0 respectively. Both these values are greater than 5.
Step 6 ：So, according to the conditions for using a normal distribution approximation for the sampling distribution of sample proportions, a normal distribution approximation can be used in this case.
Step 7 ：Final Answer: The values of np and n(1-p) are \(\boxed{39.0}\) and \(\boxed{111.0}\) respectively. Yes, a \(\boxed{\text{normal distribution approximation can be used}}\) for the sampling distribution of sample proportions.
