Light bulbs supplied by a certain company have a length life that is approximately normally distributed, with the standard deviation of 40 hours. If a random sample of 36 bulbs has an average life of 780 hours, find a 95% confidence interval for the population mean of all bulbs supplied by this company. Give the lower boundary.

1 answer

To calculate the 95% confidence interval for the population mean of all bulbs supplied by the company, we can use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / sqrt(sample size))

First, we need to determine the critical value. In a normal distribution, the critical value for a 95% confidence interval is approximately 1.96.

Next, we plug in the given values into the formula:

Confidence interval = 780 ± (1.96 * 40 / sqrt(36))

Simplifying this expression:

Confidence interval = 780 ± (1.96 * 40 / 6)

Confidence interval = 780 ± 27.87

To find the lower boundary of the confidence interval, we subtract 27.87 from the sample mean:

Lower boundary = 780 - 27.87

Lower boundary ≈ 752.13

Therefore, the lower boundary of the 95% confidence interval for the population mean of all bulbs supplied by the company is approximately 752.13.