A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of homeowners selected from this area showed that they pay an average of per month for their mortgages. The population standard deviation of such mortgages is . a. Find a confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. Round your answers to two decimal places. 1538.51 to 1627.49 dollars b. Suppose the confidence interval obtained in part a is too wide. Select all of the ways the width of this interval can be reduced.

Complete Question

The complete question is shown on the first uploaded image

a

The  97% confidence interval is  

b

Option A and  Option D  are correct

Step-by-step explanation:

From the question we are told that

     The sample size is n =  119

     The  sample  mean is

    The  population standard deviation is  

    Generally given that the confidence level is  97% then the level of significance is mathematically represented as

=>    

From the normal  distribution table  the critical value  of   is  

Generally the margin of error is mathematically represented as

=>  

Generally the 97% confidence interval is mathematically represented as

=>    

=>    

Generally looking at confidence interval we see that the width is dependent on the size of the margin of error.

Generally the margin error is directly proportional to the  critical value of   which increases when the confidence level increases and vise versa

Also the margin error is inversely proportional to the square root of  sample size

Hence to reduce the width of the confidence interval we need to lower the confidence level  and increase the sample size

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you