The grades of a group of 1000 students in an exam are normally distributed with a mean of 70 and a standard deviation of 10. A student from this group is selected randomly.

a) Find the probability that his/her grade is greater than 80.

b) Find the probability that his/her grade is less than 50.

c) Find the probability that his/her grade is between 50 and 80.

d) Approximately, how many students have grades greater than 80?

RainielFornolesTyro

This answer was edited.Let be a random variable representing the grade of a student in the exam, then the probability that is less than a value, , is equivalent to the area under the standard normal curve with -score given by , where is the mean/average and is the standard deviation.

Here, and .

a.) Thus, . Using the table of areas under the standard normal curve or a calculator, we have .

b.) . Using the table of areas under the standard normal curve or a calculator, we have .

c.)

. Using the table of areas under the standard normal curve or a calculator, we have .

d.) From (a), P(X > 80) = 0.15866. Thus, given that there are 1000 students, the number of students expected to have a grade greater than 80 is students.