A manufacturer of watches has established that on the average his watches do not gain or lose. He also would like to claim that at least 95% of the watches are accurate to 0.2 s per week. A random...

A manufacturer of watches has established that on the average his watches do not gain or lose. He also would like to claim that at least 95% of the watches are accurate to
0.2 s per week. A random sample of 15 watches provided the following gains (+) or losses (-) in seconds in 1 week:

+ 0.17 - 0.07 + 0.13 - 0.05 + 0.23

+ 0.01 + 0.06 + 0.08 - 0.14 + 0.10

+ 0.08 + 0.11 + 0.05 - 0.87 + 0.05

Can the claim be made with a 5% chance of being wrong? (Assume that the inaccuracies of these watches are normally distributed.)