Question

Computer Services, Inc. wants to determine a confidence interval for the average CPU time of their teleprocessing transactions. A sample of 51 transactions yielded a mean of 5 seconds. The population standard deviation is 2.4 seconds. Determine a 95% confidence interval for the average CPU time.

Answer 1

Answer:

The 95% confidence interval for the average CPU time is between 4.34 hours and 5.66 hours.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$.

So it is z with a pvalue of $1-0.025 = 0.975$, so $z = 1.96$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{2.4}{\sqrt{51}} = 0.66$

The lower end of the interval is the sample mean subtracted by M. So it is 5 - 0.66 = 4.34 hours.

The upper end of the interval is the sample mean added to M. So it is 5 + 0.66 = 5.66 hours

The 95% confidence interval for the average CPU time is between 4.34 hours and 5.66 hours.