contestada

mr. emmer gave a test in his chemistry class. the scores were normally distributed with a mean of 82 and a standard deviation of 4. what percent of students would you expect to score between 78 and 36?

Respuesta :

[tex]P(36\le X\le78)=P(\frac{X1-\mu}{\sigma}\le Z\le\frac{X2-\mu}{\sigma})[/tex]

Where:

[tex]\begin{gathered} X1=36 \\ X2=78 \\ \mu=82 \\ \sigma=4 \end{gathered}[/tex]

So:

[tex]\begin{gathered} P(36\le X\le78)=P(\frac{78-82}{4}\le Z\le\frac{86-82}{4}) \\ P(36\le X\le78)=P(-1\le Z\le1) \\ P(36\le X\le78)=0.6827\approx0.68 \end{gathered}[/tex]

As a percentage: 68%

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