[See Steps] SAT scores. The total SAT scores of high school seniors in recent years have mean μ=1026 and standard deviation σ=209. The distribution
Question: SAT scores. The total SAT scores of high school seniors in recent years have mean \(\mu=1026\) and standard deviation \(\sigma=209\). The distribution of SAT scores is roughly Normal.
- Ramon scored 1100 . If scores have a Normal distribution, what percentile of the distribution is this? (That is, what percent of scores are lower than Ramon's?)
- Now consider the mean \(\bar{x}\) of the scores of 70 randomly chosen students. If \(\bar{x}=1100\), what percentile of the sampling distribution of \(\bar{x}\) is this?
- Which of your calculations, (a) or (b), is less accurate because SAT scores do not have an exactly Normal distribution? Explain your answer.
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