Question: Q1. Two students (who were thrilled with the Central Limit Theorem for

Question

Question:

Q1. Two students (who were thrilled with the Central Limit Theorem for the sample mean) have looked at all possible samples of size 25 from the population of students in their class. For each of those samples, the two students have also recorded the corresponding average age. Pick the FALSE statement among the following three:

a: The distribution of the average age of students in all samples of size 25 has a mean which is equal to the average age of a student in their class.

b: The distribution of the average age of students in all samples of size 25 has a standard deviation which is smaller than the standard deviation of the ages of students in their class.

c: The distribution of the average age of students in all samples of size 25 is the same as the distribution of the ages of students in their class.

Q2 Peter decides to study the distribution of the daily demand for a newspaper in a small town in Italy. Based on historical data, he constructed the histogram of daily demand which is given by the graph (see attachment)

Q A Peter is considering to use a normal distribution to accurately approximate the distribution of daily demand described by the figure above. Which of the following statements is correct?

a: Peter can claim that the normal distribution is a good approximation since the histogram displays two bell shaped curves.

b: Peter can claim that he can find a normal distribution that will approximate nicely this histogram by adjusting both the mean and variance properly.

c: Peter cannot claim the normal approximation is good in this case because the distribution does not put probability mass on have negative values.

d: Peter cannot claim that the normal distribution is a good approximation since the histogram shows a distribution that is quite different from a normal distribution that it is not even close to being symmetric around its mean.

Q B Now suppose that Peter is considering using a normal distribution to accurately approximate the distribution of the average daily demand over the whole year. Which of the following statements is true?

a: Peter cannot do that since he cannot use a normal distribution to accurately approximate the daily demand in a particular day.

b: Peter can do that since he can accurately approximate the daily demand using a normal distribution

c: Peter cannot do that since the average demand will not be exactly symmetric around its mean

d: Peter can do that because of the central limit theorem.

Explanation / Answer

dear student, please post the question one at a time.

1)option C is right.

The central limit theorem states that when samples from a data set with a known variance are aggregated their mean roughly equals the population mean. Said another way, CLT is a statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population

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