It is known that the average American spends $121 per month on eating out. Which of the following needs to be satisfied in order to be able to use the Central Limit Theorem to describe the sampling distribution of the average amount of money Americans spend eating out? The sample needs to be representative of all Americans. The amount of money Americans spend eating out needs to be normally distributed. The sample size should not be less than 30. The expected numbers of those who do and do not eat out needs to both be at least 5. Answer Choices: 1 and 2 1 and 3 1, 2, and 3 1, 2, 3, and 4 1 and either 2 or 3
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
It is known that the average American spends $121 per month on eating out. Which of the following needs to be satisfied in order to be able to use the Central Limit Theorem to describe the sampling distribution of the average amount of money Americans spend eating out?
- The sample needs to be representative of all Americans.
- The amount of money Americans spend eating out needs to be
normally distributed. - The sample size should not be less than 30.
- The expected numbers of those who do and do not eat out needs to both be at least 5.
Answer Choices:
- 1 and 2
- 1 and 3
- 1, 2, and 3
- 1, 2, 3, and 4
- 1 and either 2 or 3
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