Question
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1700 hours and a standard deviation of 40 hours. What percentage light bulbs last more than 1680 hours, to the nearest tenth?
Answers
GPT 3.5
To find the percentage of light bulbs that last more than 1680 hours, we need to find the z-score for 1680 hours and then find the percentage of data that falls above this z-score in a standard normal distribution table.
First, calculate the z-score:
Z = (X - μ) / σ
where X = 1680 hours, μ = 1700 hours, and σ = 40 hours
Z = (1680 - 1700) / 40
Z = -0.5
Next, find the percentage of data that falls above a z-score of -0.5 in a standard normal distribution table. Looking up the z-score in the table or using a calculator, we find that the percentage is 69.15%.
Therefore, approximately 69.15% of light bulbs last more than 1680 hours.
First, calculate the z-score:
Z = (X - μ) / σ
where X = 1680 hours, μ = 1700 hours, and σ = 40 hours
Z = (1680 - 1700) / 40
Z = -0.5
Next, find the percentage of data that falls above a z-score of -0.5 in a standard normal distribution table. Looking up the z-score in the table or using a calculator, we find that the percentage is 69.15%.
Therefore, approximately 69.15% of light bulbs last more than 1680 hours.