Failure times for two machines at the Babel tire factory in Iraq were obtained and used to estimate mean failure time. (Iraqi Journal of Statistical Science, Vol. 14, 2008.) The data (in hours) for the cutting layers machine and the coating machine are listed in the accompanying table. Failure time is known to follow an exponential probability distribution.

a. Find and interpret a 90% confidence interval for the mean failure time of the cutting layers machine.

b. Find and interpret a 90% confidence interval for the mean failure time of the coating machine.

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TIREIRAQ Cutting Machine: 1.00 1.00 5.00 5.50 12.50 16.75 17.75 20.75 22.50 22.75 25.00 25.00 27.25 30.25 43.75 45.00 48.00 48.25 97.50 99.75 136.75 143.50 207.75 215.000 225.50 235.00 283.50 567.00 970.50 Coating Machine: 3.5 6.5 10.5 23.25 23.5 43.5 69 70.5 75.5 83.25 95.5 109.5 111.25 144 164 167.25 253 383.75 417.75 428.25 453 1215