Construct a 99% confidence interval for life expectancy of a new GE light bulb. 64 bulbs are randomly selected and a mean of 750 hours and a standard deviation of 20 hours is found. Assume the distribution of life expectancy is normally distributed.
To construct a 99% confidence interval for the life expectancy of a new GE light bulb, we will use the formula:
CI = X̄ ± Z * (σ/√n)
Where:
- CI represents the confidence interval
- X̄ is the sample mean
- Z is the confidence level (related to the desired confidence interval: for 99% confidence, Z = 2.576)
- σ is the population standard deviation
- n is the sample size
Given the information in the question:
- The sample mean (X̄) is 750 hours
- The standard deviation (σ) is 20 hours
- The sample size (n) is 64
- The desired confidence level is 99% (Z = 2.576)
Now, let's substitute the values into the formula:
CI = 750 ± 2.576 * (20/√64)
Calculating the values inside the parentheses:
CI = 750 ± 2.576 * (20/8)
Simplifying further:
CI = 750 ± 2.576 * 2.5
CI = 750 ± 6.44
Therefore, the 99% confidence interval for the life expectancy of a new GE light bulb is approximately (743.56, 756.44) hours.