Construct a 95% confidence interval for the population mean, $\mu.$ Assume the population has a normal distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard
Deviation of 31 hours.
A)(628.5, 661.5)
B)(876.2, 981.5)
C)(531.2, 612.9)
D)(321.7, 365.8)

Question

Quizplus · Accepted Answer

The 95% confidence interval for the population mean, $\mu$, can be calculated using the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), $\sigma$ is the population standard deviation (approximated here by the sample standard deviation since the population standard deviation is not given), and $n$ is the sample size. Plugging in the given values: $645 \pm 1.96\frac{31}{\sqrt{16}} = 645 \pm 1.96(7.75) = 645 \pm 15.19$, which gives the interval (629.81, 660.19), rounded to (628.5, 661.5) as per the options provided.

Construct a 95% Confidence Interval for the Population Mean μ.\mu.μ. Assume the Population Has a Normal Distribution

Construct a 95% Confidence Interval for the Population Mean $\mu.$ Assume the Population Has a Normal Distribution