Question

A light bulb has an expected life of 5000 hours, with a standard deviation of 133 hours. What is the probability that a light bulb will fail between 4,900 and 5,068 hours?

Answer 1

Mean = μ = 5000 hours

Standard Deviation = σ = 133 hours

Probability that a light bulb will fail after X hours = P(z)

where, z = (X - μ)/σ

When X1 = 4900, z = (4900 - 5000)/133 = -0.7519
From z table, P(X1) = 0.2261 or 22.61%

When X2 = 4900, z = (5068 - 5000)/133 = 0.5113
From z table, P(X2) = 0.6954 or 69.54%

Probability that the bulb will fail between 4900 hours and 5068 hours = P(X2) - P(X1) = 69.54 - 22.61 = 46.93%