contestada

The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10. What percentage of the scores are greater than 87? 34% 50% 84% 16%

Respuesta :

Given

[tex]\begin{gathered} \mu=77 \\ \sigma=10 \end{gathered}[/tex]

The z-score formula is

[tex]z=\frac{x-\mu}{\sigma}[/tex]

In our case,

[tex]\Rightarrow z=\frac{87-77}{10}=\frac{10}{10}=1[/tex]

Using a z-score table,

[tex]\Rightarrow P(X<87)=0.8413[/tex]

Then,

[tex]\begin{gathered} P(X>87)=1-P(X<87)=1-0.8413=0.1587=15.87\% \\ \Rightarrow P(X>87)\approx16\% \end{gathered}[/tex]

Thus, the answer is 16%

Otras preguntas