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

Step-by-step 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: $z=\dfrac{x-\mu}{\sigma}$

For x=82

$z=\dfrac{82-72.3}{8.9}\approx1.09$

For x=90

$z=\dfrac{90-72.3}{8.9}\approx1.99$

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

$P(82$

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

$184\times0.1146=21.0864\approx21$

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