There are 440 students at Thomas Paine high school enrolled in U.S. history. On the April report card, the students’ grades are approximately normally distributed with a mean of 79 and a standard deviation of 7. Students who earn a grade less than or equal to 62.9 must attend summer school Rounded to the nearest whole number ,how many students who must attend summer school for U.S. history?

Respuesta :

Answer:

5 students.                  

Step-by-step explanation:

We have been given that there are 440 students at Thomas Paine high school enrolled in U.S. history. On the April report card, the students’ grades are approximately normally distributed with a mean of 79 and a standard deviation of 7. Students who earn a grade less than or equal to 62.9 must attend summer school.

To find the number of students who must attend summer camp let us find x-score for our given sample score 62.9.

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

[tex]x[/tex] = Sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{62.9-79}{7}[/tex]    

[tex]z=\frac{-16.1}{7}[/tex]

[tex]z=-2.3[/tex]

Now we will use the normal distribution table to find [tex]P(z<-2.3)[/tex].

[tex]P(z<-2.3)=0.01072 [/tex]        

Since the probability of a student getting grade less than 62.9 is 0.01072, so we will multiply 0.01072 by the 440 to get the number of students, who must attend summer school for history.

[tex]\text{Number of students, who must attend summer school for U.S. history}=0.01072\times 440[/tex]

[tex]\text{Number of students, who must attend summer school for U.S. history}=4.7168\approx 5[/tex]  

Therefore, 5 students must attend summer school for U.S. history.  

I’m taking this test right now and the answer is 10.

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