Question

Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 675 and 900 hours.

Answer 1

To find the probability that a randomly selected light bulb will last between 675 and 900 hours, we need to standardize the values using the z-score formula and look up the corresponding probabilities in the standard normal distribution table. The probability is 0.8185.

Step-by-step explanation:

To find the probability that a randomly selected light bulb will last between 675 and 900 hours, we need to find the area under the bell-shaped curve of the normal distribution.

First, we need to standardize the values using the z-score formula: z = (x - mean) / standard deviation. For 675 hours: z = (675 - 750) / 75 = -1.0. For 900 hours: z = (900 - 750) / 75 = 2.0.

Next, we can look up the probabilities corresponding to these z-scores in the standard normal distribution table. The probability for a z-score of -1.0 is 0.1587, and the probability for a z-score of 2.0 is 0.9772.

Finally, we can subtract the probability of the lower value from the probability of the higher value to find the probability that a randomly selected light bulb will last between 675 and 900 hours: 0.9772 - 0.1587 = 0.8185.