The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.

What is the correct interpretation of the confidence interval?

Select the correct answer below:

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

2. We can estimate with 99% confidence that the sample mean length of adult corn snakes is between 53.88 and 62.12 inches.

3. We can estimate that 99% of adult corn snakes will have a length that is between 53.88 and 62.12 inches.

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

Step-by-step explanation:

With the data that, we have, we can estimate the 99% confidene interval for the true population mean.

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

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

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

The lower end of the interval is the sample mean subtracted by M. So it is 58 - 4.12 = 53.88 inches.

The upper end of the interval is the sample mean added to M. So it is 58 + 4.12 = 62.12 inches

So the correct answer is:

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

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