The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points. About what percent of students have scored between 60 and 65 points?

Using Empirical Rule (68 - 95 - 99.7 Rule), 68% of the data lies in between 1 standard deivation from the mean so since you are not doing 55 to 65 and instead 60 to 65, you divide 68 by 2 and you get 34%.

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JeanaShupp JeanaShupp · Answer 2 · 2020-03-22T04:05:30+01:00

Answer: The percent of students have scored between 60 and 65 points is 34.13%

Step-by-step explanation:

Given : The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.

i.e. [tex]\mu=60\ \ \ \sigma=5[/tex]

Let x denotes the points obtained by students of a class in a test .

Now , the probability that the students have scored between 60 and 65 points :-

[tex]P(60<x<65)=P(\dfrac{60-60}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{65-60}{5})\\\\= P(0<z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\= P(z<1)-P(z<0.5)\ \ \ [\because\ P(z_1<Z<z_2)=P(Z<z_2)-P(Z<z_1)]\\\\=0.8413-0.5=0.3413[/tex]

[tex]=34.13\%[/tex]

Hence, the percent of students have scored between 60 and 65 points is 34.13%.