For each simulated null distribution, indicate whether or not a normal distribution would be a reasonable approximation.
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2:
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5:
6:

Question

For each simulated null distribution, indicate whether or not a normal distribution would be a reasonable approximation.
1: 
2: 
3: 
4: 
5: 
6:

BlackTom AI · Accepted Answer

The prompt asks me to indicate, for each of six simulated null distributions, whether a normal distribution would be a reasonable approximation. However, the provided data does not include the actual distributions or their descriptive details (no histograms, no summary statistics beyond a stray image, and the answer key/options are missing or incomplete). Because of this, I cannot assign yes or no to each specific distribution with confidence.

Here is a general framework you can apply once you have the distributions or their summaries:
- When is a normal approximation reasonable for a null distribution of a proportion (or a mean)?
  • Large sample size: as n grows, sampling distributions tend to be more Normal by the Central Limit Theorem.
  • Proportions: both np and n(1-p) should be reasonably large (commonly np ≥ 10 and n(1-p) ≥ 10) for the normal approximation to be appropriate.
  • Shape indicators: a roughly bell-shaped, symmetric histogram around the mean supports normality; skewness or heavy tails suggest poor fit.
  • If the data come from a binomial or proportion scenario with p near 0 or 1 and small n, the Normal approximation may be inadequate; a Poisson or exact binomial approach might be preferred.
  • For many simulated nulls, if the histograms look symmetric and unimodal with gradual tails, a normal approximation is typically reasonable; if they look skewed, multimodal, or severely kurtotic, it is not.

Given the missing options and data, I cannot complete the required yes/no judgments for each of the six items. To proceed, please provide:
- The six distributions (or their summaries, e.g., means, standard deviations, sample sizes, or p-values), and/or
- The actual answer options and the corresponding mapping to each distribution.
Then I can produce a precise, itemized justification for why each distribution should be approximated by a normal or not, with varied explanatory phrasing for each item.

Su25-STATS-141-01/BIO-141-01 1.3 - 1.5 Readiness Quiz

For each simulated null distribution, indicate whether or not a normal distribution would be a reasonable approximation. 1: 2: 3: 4: 5: 6:

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