Question

The life of a fully-charged cell phone battery is normally distributed with a mean of 14 hours with a standard deviation of 3 hours. What is the probability that 25 batteries last at least 13 hours?

Answer 1

Here, μ = 14, σ = 0.6 and x = 13. We need to compute P(X >= 13). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (13 - 14)/0.6 = -1.67

Therefore,
P(X >= 13) = P(z <= (13 - 14)/0.6)
= P(z >= -1.67)
= 1 - 0.0475 = 0.9525