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: 21Step-by-step explanation:Given : The scores on the midterm exam are normally distributed with[tex]\mu=72.3\\\\\sigma=8.9[/tex]Let X be random variable that represents the score of the students. z-score: [tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x=82[tex]z=\dfrac{82-72.3}{8.9}\approx1.09[/tex]For x=90[tex]z=\dfrac{90-72.3}{8.9}\approx1.99[/tex]Now, the probability of the students in the class receive a score between 82 and 90 ( by using standard normal distribution table ) :-[tex]P(82<X<90)=P(1.09<z<1.99)\\\\=P(z<1.99)-P(z<1.09)\\\\=0.9767-0.8621=0.1146[/tex]Now ,the number of students expected to receive a score between 82 and 90 are :-[tex]184\times0.1146=21.0864\approx21[/tex]Hence, 21 students are expected to receive a score between 82 and 90 .