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. Identify the parameters needed to calculate a confidence interval at the 99% confidence level. Then find the confidence interval.

Parameters: z = 2.575

The 99% confidence interval for the lengths, in inches, of adult corn snakes are between 53.88 inches and 62.12 inches.

Step-by-step explanation:

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.

The 99% confidence interval for the lengths, in inches, of adult corn snakes are between 53.88 inches and 62.12 inches.

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