Question

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 75 hours. What is the probability that a randomly chosen light bulb will last less than 1380 hours, to the nearest thousandth?

Answer 1

To find the probability that a randomly chosen light bulb will last less than 1380 hours, you can calculate the z-score using the mean and standard deviation and then use the standard normal distribution table or calculator to find the probability. The probability is approximately 0.394 or 39.4%.

Step-by-step explanation:

To find the probability that a randomly chosen light bulb will last less than 1380 hours, we need to calculate the z-score and then use the standard normal distribution table.

First, we calculate the z-score: z = (x - mean) / standard deviation = (1380 - 1400) / 75 = -0.267.

Next, we use the standard normal distribution table or a calculator to find the probability associated with this z-score.

Using the z-score table or calculator, we find that the probability of a randomly chosen light bulb lasting less than 1380 hours is approximately 0.394 or 39.4%.