Question

9.) Now, you can also check the calculation you did in #7, by typing the following command: "BINOM.DIST(2,3,.25,1)", which means you want to get two correct (# of successes) out of three items (# of trials), where the probability of getting one item correct is .25 (probability of a success), and we are adding up the probabilities for all values below 2 as well (the cumulative spot is turned on when you type "1").

1. What is the difference between a frequency distribution and a sampling distribution?
2. Describe the circumstances under which the Central Limit can/should be applied. For example: imagine you were talking to a classmate who needs help with this topic. How do you know when to use the Central Limit Theorem.
3. Describe how to use the Central Limit Theorem. That is, what about using it is the same as previous work you've done? What about it is different?

Answer 1

9. P(X = 0) =BINOM.DIST(0, 3, 0.25, TRUE) = 0.421875

P(X = 1) = BINOM.DIST(1, 3, 0.25, TRUE) = 0.84375

P(X = 2) = BINOM.DIST(2, 3, 0.25, TRUE) = 0.984375

P(X = 3) = BINOM.DIST(3, 3, 0.25, TRUE) = 1

10. The histogram is:

• sampling distribution: The probability distribution of a given statistic based on a random sample.
• frequency distribution: a representation, either in a graphical or tabular format, which displays the number of observations within a given interval

• Randomization Condition: The data must be sampled randomly.
• Independence Assumption: The sample values must be independent of each other.
• 10% Condition: When the sample is drawn without replacement (usually the case), the sample size, n, should be no more than 10% of the population.

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.