Reference no: EM132846591
1. Suppose we somehow know that for the population of all Purdue undergraduate students, the mean age is 22.0 years, with a standard deviation of 4.0 years.
a) Would you expect ages of Purdue undergraduates to be normally distributed? Explain your reasoning. Consider the popularity of going to college at a variety of different ages.
b) We plan to collect random samples of 36 students and compute the sample mean age, ??¯ , for each sample. Would you expect the sampling distribution of ??¯ , to be normally distributed? Explain briefly.
c) In approximately what proportion of samples would ??¯ be between 21.8 and 22.2 years?
d) Now suppose that the sample size is increased to 50 students per sample. In what proportion of samples would ??¯ be between 21.8 and 22.2 years?
2. A certain supplement advertises 125 mg of vitamin D per capsule, although the actual amount varies slightly according to a normal distribution with a mean of 125 mg and standard deviation of 0.8 mg.
a) What proportion of capsules have between 124.5 and 125.5 mg of vitamin D?
b) Suppose you take a capsule daily for 7 days. What is the probability that on average you receive between 124.5 and 125.5 mg of vitamin D?
c) Was it necessary to use the Central Limit Theorem to answer part b? Why or why not?
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: 1. Suppose we somehow know that for the population of all Purdue undergraduate students, the mean age is 22.0 years, with a standard deviation of 4.0 years.
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