The lifetime of a certain brand of battery is known to have a standard deviation of

19.8

hours. Suppose that a random sample of

90

such batteries has a mean lifetime of

36.4

hours. Based on this sample, find a

90%

confidence interval for the true mean lifetime of all batteries of this brand. Then give its lower limit and upper limit.

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