Question

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 600 hours. Find the probability of a bulb lasting for at most 630 hours. Round your answer to four decimal places.

Answer 1

We are given the following information

Mean lifetime of a bulb = 600 hours

Standard deviation of the lifetime of a bulb = 20 hours

P(X ≤ 630) = ?

At most 630 hours means equal to or less than 630 hours.

Since the life of light bulbs is normally distributed, we can calculate the probability using the z-score.

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{630-600}{20} \\ z=1.50 \end{gathered}$

From the z-table, the probability corresponding to the z-score of 1.50 is found to be 0.9332

$\begin{gathered} P(X\le630)=P(z<1.50) \\ P(X\le630)=0.9332 \end{gathered}$

Therefore, the probability of a bulb lasting for at most 630 hours is 0.9332