The university data center has two main computers. The center wants to examine whether computer

1

is receiving tasks that require processing times comparable to those of computer

2

. A random sample of

15

processing times from computer

1

showed a mean of

65

seconds with a standard deviation of

20

seconds, while a random sample of

10

processing times from computer

2

(chosen independently of those for computer

1

) showed a mean of

58

seconds with a standard deviation of

19

seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a

99%

confidence interval for the difference

12

between the mean processing time of computer

1

,

1

, and the mean processing time of computer

2

,

2

. Then find the lower limit and upper limit of the

99%

confidence interval.

Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)