Below is one question with two parts Q Peter decides to study the distribution o
ID: 3071590 • Letter: B
Question
Below is one question with two parts
Q 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.
0.12 0.1 0.08 0.06 A- 0.04 0.02 I1 120 130 140 150 160 170 Values of XExplanation / Answer
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?
Ans:
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?
Ans: d: Peter can do that because of the central limit theorem.
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