A local service agency hires you to estimate the average annual income of all 700 families living in a four square block section. Since time and funds are limited, yu take a random sample of 50 families and want the estimate to have a 92% confidence level. The 50 families had an average income of $35,300. Research shows the population standard deviation for annual income in this four square block section is $1,800

The true estimate of  the average annual income of all 700 families living in a four square block section lies within the 92% confidence interval below

Step-by-step explanation:

From the question we are told that

    The  sample size is  n =  50  

    The sample mean is

     The population standard deviation is  

From the question we are told the confidence level is  92% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

=>  

=>  

Generally 92% confidence interval is mathematically represented as  

=>

=>

So the true estimate of  the average annual income of all 700 families living in a four square block section lies within the 92% confidence interval

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)