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.