Step 1 :Calculate the Z-score using the formula: \(Z = \frac{X - \mu}{\sigma}\)
Step 2 :Substitute the given values into the formula: \(Z = \frac{550 - 500}{40} = 1.25\)
Step 3 :Look up the probability that the Z-score is less than 1.25 in the standard normal distribution table (Z-table), which is approximately 0.8944
Step 4 :Calculate the probability that the Z-score is more than 1.25 using the formula: \(1 - P(Z < 1.25)\)
Step 5 :Substitute the value from the Z-table into the formula: \(1 - 0.8944 = 0.1056\)
Step 6 :\(\boxed{0.1056}\) is the probability that an Endure All battery selected at random will last more than 550 hours