Question

A company owns rental properties and must pay for repairs and upkeep. If the monthly maintenance costs have an average of $3500.00 and a standard deviation of $257.00, give the range of costs the company can count on having to pay about 95% of the time.

Answer 1

(2996.28, 4003.72)

is 95% range.

Explanation:

Given is -

the monthly maintenance costs have an average of $3500 and a standard deviation of $257.

If X denotes the monthly maintenance costs of the company then

X is N(3500,257)

To find out 95% of the range we have Z critical = 1.96

So lower bound of range
`= 3500-1.96*257` and

Upper bound
`= 3500+1.96*257`

Hence, range becomes :

(2996.28, 4003.72)

Answer 2

Given is - the monthly maintenance costs have an average of $3500 and a standard deviation of $257. This means that around 95% of the distributed data lies within the ranges of -257 to +257 of the given standard deviation.

Hence, range becomes :

`3500-257=3243` and
`3500+257=3757`

Thus, the range is (3243 , 3757)