In an analysis investigating the usefulness of pennies, the cents portions of 100 randomly selected credit card charges from the author are recorded they have a mean of 47.6 cents and a standard deviation of 33.5 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents if the amounts from 0 to 99 cents are all equally likely is the requirement of a normal distribution satisfied? If not how does that affect the conclusion?

Test the given claim. Identify the null hypotheis, alternative hypothoses, test statistic, P value or critical values, conclusion about the null hypothesis, and final conclusion that address the original claim. Assume that at simple random sample is slected from a normally distributed population.