Question
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 2000 hours and a standard deviation of 70 hoursWhat percentage light bulbs last more than 2110 hours, to the nearest tenth?
Answers
GPT 3.5
To find the percentage of light bulbs that last more than 2110 hours, we need to calculate the z-score for 2110 hours and then find the area to the right of that z-score.
The z-score is calculated as follows:
z = (X - μ) / σ
z = (2110 - 2000) / 70
z = 0.1571
Now, we look up the z-score in the standard normal distribution table or use a calculator to find the percentage corresponding to a z-score of 0.1571. This percentage represents the percentage of light bulbs that last more than 2110 hours.
Using a standard normal distribution table or calculator, we find that the percentage of light bulbs that last more than 2110 hours is approximately 44.0% to the nearest tenth.
The z-score is calculated as follows:
z = (X - μ) / σ
z = (2110 - 2000) / 70
z = 0.1571
Now, we look up the z-score in the standard normal distribution table or use a calculator to find the percentage corresponding to a z-score of 0.1571. This percentage represents the percentage of light bulbs that last more than 2110 hours.
Using a standard normal distribution table or calculator, we find that the percentage of light bulbs that last more than 2110 hours is approximately 44.0% to the nearest tenth.