Question

A) According to a survey it takes .7 second to download the home page website. Suppose that the download was normally distributed with a standard deviation of .2.

If you select a random sample of 23 download times, the probability is 85% that the sample mean is between what two values symmetrically distributed around the population mean?

Lower Bound:

Upper Bound:

Answer 1

Here confidence level = 85%

So, $\alpha$ = 0.15

Now, $z_{\alpha/2}$ = 1.44

Lower Bound

$= \bar x - z_{\alpha/2} \frac{\sigma}{\sqrt n} = 0.7 - 1.44 * \frac{0.2}{\sqrt {23}} = 0.6399$

Upper Bound

$= \bar x + z_{\alpha/2} \frac{\sigma}{\sqrt n} = 0.7 + 1.44 * \frac{0.2}{\sqrt {23}} = 0.7601$

** If the answer does not match please comment