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.
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.
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