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Since we know the population standard deviation and the sample size is above 30, then we use the z statistic. The formula for z score is:

z = (x – u) / s

where,

x = the sample mean or sample value = 8.6 hours

u = the population mean = 8.4 hours

s = the standard deviation = 1.8 hours

Substituting into the given equation:

z = (8.6 – 8.4) / 1.8

z = 1.11

Using the standard probability distribution tables for z, a value of z = 1.11 has a probability of:

p = 0.8665

However this is still not the correct answer since this refers to the left of z. What we are trying to find is to the right of z since problem ask for exceeds 8.6 hours, therefore the correct answer is:

P (x>8.6 hours) = 1 – 0.8665

P (x>8.6 hours) = 0.1335

Therefore there is a 13.35% chance that the mean rebuild time is greater than 8.6 hours.