Question

the accompanying histogram shows the distribution of mean composite scores for a regions public schools with schools from school district m and several alternative schools removed. the vertical lines show the mean, mean - 1s, and mean + 1s. complete parts a through d below.
click here to view the distribution of the mean composite scores.
click here to view the distribution of the mean composite scores with the normal curve.

c) approximately 65.7% of the school average scores are between the two outer lines. does that support or refute your answer to part b?
the percentage of schools that are between the two outer lines supports the answer to part b because about 68% of the data is expected to be within one standard deviation of the mean.
d) a normal model with mean 22.2 and standard deviation 1.5 is drawn over the histogram. explain how this demonstrates george boxs statement, \all models are wrong - but some are useful.\
choose the correct answer below.
a. the model is not correct because the bars extend above the model in most locations. the model is a smooth, continuous curve but the bars are discrete. the model does not give good estimates of the test scores in most ranges.
b. the model is not correct because the bars extend below the model in most locations. the model is a smooth, continuous curve but the bars are discrete. however, the model will give close estimates of the test scores in a few locations.
c. the model is correct because the heights of the bars are close to the model. the model and bars are smooth, continuous curves and the model provides exact estimates of the test scores in most ranges.
d. the model is not correct because in some locations the bars extend above the model and in other places they are below it. the model is a smooth, continuous curve but the bars are discrete. however, the model will give close estimates of the test scores in some ranges.

Explanation:

For part c, in a normal distribution, approximately 68% of the data lies within one standard deviation of the mean. If about 65.7% of school - average scores are between the two outer lines (which are mean ± 1s, assuming the outer lines represent one - standard - deviation bounds), this is close to the 68% expected in a normal distribution. So it supports the idea that the distribution is approximately normal (from part b answer A: "Yes because the distribution is reasonably symmetric and bell - shaped").

Answer:

It supports the answer to part b. Since in a normal distribution, about 68% of data is within one standard deviation of the mean, and 65.7% is close to 68%, it indicates that the data has a distribution pattern similar to a normal distribution (supports the claim that the distribution is reasonably symmetric and bell - shaped as in part b answer A).