Question

A company that produces white bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice. Construct a 99% confidence interval for the unknown mean sodium level assuming that the population standard deviation is 10 milligrams.

Answer 1

Answer:

The 99% confidence interval for the unknown mean sodium level is between 100.42 milligrams of sodium per slice and 105.58 milligrams of sodium per slice.

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:

$\alpha = \frac{1 - 0.99}{2} = 0.005$

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

That is z with a pvalue of $1 - 0.005 = 0.995$, so Z = 2.58.

Now, find the margin of error 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.

$M = 2.58\frac{10}{\sqrt{10}} = 2.58$

The lower end of the interval is the sample mean subtracted by M. So it is 103 - 2.58 = 100.42 milligrams of sodium per slice.

The upper end of the interval is the sample mean added to M. So it is 103 + 2.58 = 105.58 milligrams of sodium per slice.

The 99% confidence interval for the unknown mean sodium level is between 100.42 milligrams of sodium per slice and 105.58 milligrams of sodium per slice.