Question

A company selling light bulbs claims in its advertisements that its light bulbs’ average life is 1000 hours. In fact, the life span of these light bulbs is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours.Find the probability that a randomly chosen light bulb will last less than 900 hours.

Answer 1

Answer:

15.87%

Step-by-step explanation:

Given that:

The mean (μ) = 1000 hours, the standard deviation (σ) = 100 hours.

The z score provides a means of measurement in statistics to determine the variation of a raw score from the mean. The z score is given as:

$z=\frac{x-\mu}{\sigma}$

To find that a randomly chosen light bulb will last less than 900 hours:

$z=\frac{x-\mu}{\sigma}=\frac{9000-1000}{100}=-1$

Therefore, P(x < 900) = P(z < -1) = 0.1587 = 15.87%