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A medical researcher believes the body temperature of adults is normally distributed with a standard deviation of 0.4oC.

a. What sample size is required such that a 99% confidence interval of mean body temperature of adults has width at most 0.06oC?

b. Based on the result in part (a), is it really necessary to assume the body temperature of adults is normally distributed? Why?

A nutrition lab tested the mean sodium content of 100 hot dogs. The lab reported that the mean sodium content of their sample is 322 mg with a standard deviation of 2.5 mg.

a. One of the aims is to report a 95% confidence interval for the mean sodium content of hot dogs. Is it necessary to assume the distribution of sodium content of hot dogs is normally distributed? Why?

b. Based on your result in part (a), obtain the 95% confidence interval for the mean sodium content of hot dogs.c. Based on the result in part (b), is there any evidence that the mean sodium content is different from the stated 325 mg on the package?d. A dietitian is interested to know if the result suggested that the mean sodium content of hot dogs is significantly lower than the stated 325 mg on the package. What can you tell from the lab results? (You answer has to be justified based on statistics concepts.)

An automatic character recognition device can successfully read about 85%of hand-written credit card application.

a. Three credits card applications are randomly selected. What is the probability that the device successfully read at least two of them?1

b. Three hundred credits card applications are randomly selected. What is the probability that the device successfully read at least two hundred of them? For this question, first given the exact expression of the required probability. Then approximate it based on the method you have learned in class (or in text).

c. What theory did you apply to obtain the answer in part (b)? Explain by the theory is applicable in this case.

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