The quality control manager at a cell phone battery factory is interested in the mean life of a large shipment of batteries.Battery life is normally distributed with a standard deviation of 100 hours.A random sample of 64 batteries indicates a sample mean of 350 hours.The 99% confidence interval for mean battery life is _____.
A)[317.8,382.2]
B)[308.9,391.1]
C)[311.4,362.5]
D)[312.5,387.5]
E)[320.9,379.1]

Question

Quizplus · Accepted Answer

We can use a t-distribution to calculate the confidence interval since the population standard deviation is unknown and our sample size is large enough (n=64) to use the central limit theorem.

The formula for the confidence interval is:

sample mean ± t-critical value(s) x standard error

First, we need to find the t-critical value(s) for a 99% confidence level with 63 degrees of freedom (64 - 1). Using a t-distribution table or calculator, we find the t-critical value to be 2.660.

Next, we need to find the standard error, which is the standard deviation of the sample distribution.

standard error = standard deviation / sqrt(sample size)

standard error = 100 / sqrt(64)

standard error = 12.5

Now we can plug in our values:

350 ± 2.660 x 12.5

350 ± 33.25

The confidence interval is [316.75, 383.25]

Rounding to one decimal place, the answer is [317.8, 382.2].

The Quality Control Manager at a Cell Phone Battery Factory