Using the Central Limit Theorem. In Exercises 5-8, assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of 1.2 kg and a standard deviation of 4.9 kg (based on Data Set 13 "Freshman 15" in Appendix B).

5. a. If 1 male college student is randomly selected, find the probability that he has no weight gain during his freshman year. (That is, find the probability that during his freshman year, his weight gain is less than or equal to 0 kg.)

b. If 25 male college students are randomly selected, find the probability that their mean weight gain during their freshman year is less than or equal to 0 kg.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

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Detailed Introduction The Central Limit Theorem CLT is a fundamental statistical concept that states that the distribution of the sample mean will be approximately normal if the sample size is suffici... View the full answer