Question

a bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. a random sample of 120 homeowners from this area showed that they pay an average of $1575 per month for their mortgages. the population standard deviation of such mortgages is $215. fins a 97% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area.

Answer 1

[ 1,532.41, 1,617.59]

Explanation:

Data provided :

Sample size, n = 120

Mean = $1,575

Standard deviation = $215

Confidence level = 97%

Now,

Confidence interval = Mean ±
`z(\sigma)/(\sqrt n)`

also,

for 97% confidence level z score = 2.17 [from standard z-table]

= $1,575 ±
`2.17\frac{215}{\sqrt {120}}`

= $1,575 ± 42.59

Therefore,

Confidence interval = [ $1,575 - 42.59, $1,575 + 42.59]

= [ 1,532.41, 1,617.59]