Assume that all the distributions are normal, average is always taken to be the arithmetic mean x^- or mu. Which of these students scored below mean?

aortiH 2021-10-04 Answered
Assume that all the distributions are normal, average is always taken to be the arithmetic mean xˉ or μ. A college Physical Education Department offered an Advanced First Air course last semester. The scores on the comprehensive final exam were normally distributed, and the the z scores for some of the students are shown below:

Robert, 1.11

Juan, 1.66

Susan, –1.9

Joel, 0.00

Jan, –0.65

Linda, 1.46

(c) Which of these students scored below the mean?

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Expert Answer

odgovoreh
Answered 2021-10-05 Author has 14684 answers
Jan and Susan both have negative z scores signifying they scored below the mean.
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Relevant Questions

asked 2021-05-25

Assume that all the distributions are normal, average is always taken to be the arithmetic mean \(\bar{x}\) or \(\mu\). A college Physical Education Department offered an Advanced First Air course last semester. The scores on the comprehensive final exam were normally distributed, and the the z scores for some of the students are shown below:

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This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function
\(\displaystyle{p}{\left({x}\right)}={\frac{{{1}}}{{\sqrt{{{2}\pi^{\sigma}}}}}}{e}-\frac{{\left({x}-\mu\right)}^{{2}}}{{{2}\sigma^{{2}}}}\)
where \(\pi\) = 3,14159265 ... and \(\sigma\) and \(\mu\) are constants called the standard deviation and the mean, respectively. Its graph (for \(\sigma=1\) and \(\mu=2)\) is shown in the figure.
With \(\displaystyle\sigma={\color{red}{{5}}}\) and \(\mu=0\), approximate \(\displaystyle{\int_{{{0}}}^{{+\infty}}}{p}{\left({x}\right)}{\left.{d}{x}\right.}\).(Round your answer to four decimal places.)

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