My Courses > CRN 40938 Chapter 6 HW - The Normal Distribution AI Category: Homework Current score: 48/100 points Submit assignment (1) 3 (4) 5 (6) 7 Current learning objective: \( z \)-Scores Question 13 Practice similar questions Prev Next Score: 0 of 2 points A factory produces light bulbs, and the lifespan of these light bulbs follows a normal distribution. The mean lifespan of a light bulb is 900 hours with a standard deviation of 110 hours. The quality control department wants to know approximately what percent of a batch of light bulbs produced have a lifespan between 680 hours and 1120 hours. Approximately what percent of this batch of light bulbs have a lifespan between 680 hours and 1120 hours? A 68 B 95 C 99.7

To tackle the problem of lifespans in light bulbs, we can use the empirical rule, also called the 68-95-99.7 rule. The normal distribution states that about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. In this scenario, since 680 hours is 2 standard deviations below the mean (900 - 2*110) and 1120 hours is 2 standard deviations above the mean (900 + 2*110), it is clear that approximately 95% of the light bulbs will have a lifespan within this range. So the answer is B: 95%. On a side note, this concept is widely used in various industries for quality control. For instance, manufacturers utilize the normal distribution to predict the lifespan of products or their likelihood of failure, ensuring customer satisfaction and minimizing returns or warranties. By understanding the distributions, companies can better manage inventory and forecast replacement needs!