Question

Under normal use conditions, the Mean Time To Failure of a heating coil can be modeled using the normal distribution with a mean of 15 months and a standard deviation of 2 months. Determine the probability that a heating coil will wear out after 10 months.

Answer 1

Here, μ = 15, σ = 2 and x = 10. We need to compute P(X >= 10). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (10 - 15)/2 = -2.5

Therefore,
P(X >= 10) = P(z <= (10 - 15)/2)
= P(z >= -2.5)
= 1 - 0.0062
= 0.9938