Question

Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 82 and 90?

Answer 1

Answer: 21

Explanation:

Given : The scores on the midterm exam are normally distributed with

`\mu=72.3\\\\\sigma=8.9`

Let X be random variable that represents the score of the students.

z-score:
`z=(x-\mu)/(\sigma)`

For x=82

`z=(82-72.3)/(8.9)\approx1.09`

For x=90

`z=(90-72.3)/(8.9)\approx1.99`

Now, the probability of the students in the class receive a score between 82 and 90 ( by using standard normal distribution table ) :-

`P(82<X<90)=P(1.09<z<1.99)\\\\=P(z<1.99)-P(z<1.09)\\\\=0.9767-0.8621=0.1146`

Now ,the number of students expected to receive a score between 82 and 90 are :-

`184*0.1146=21.0864\approx21`

Hence, 21 students are expected to receive a score between 82 and 90 .