Question

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?

Answer 1

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.

$z=\frac{x-\mu}{\sigma}$, where,

$x$ = Sample score,

$\mu$ = Mean,

$\sigma$ = Standard deviation.

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

$z=\frac{62.9-79}{7}$    

$z=\frac{-16.1}{7}$

$z=-2.3$

Now we will use the normal distribution table to find $P(z<-2.3)$.

$P(z<-2.3)=0.01072$        

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.

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

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

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

Answer 2

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