Answer to Question #180063 in Statistics and Probability for veahna gubatina

Question

if all the students with an iq of 87 and lower will be required to attend the remedial program, how many are they?

Answer 1

The office for admission of XYZ University found out that the IQ of incoming 1200 freshmen normally

distributed with a mean of 108 and a standard deviation of 10.

So, according to question:

Mean $\mu=108$

Standard Deviation $\sigma=10$

n= 1200

$P(X<87)=\dfrac{x-\mu}{\sigma}=\dfrac{87-108}{10}=-2.1$

P(z<-2.1)=0.0179

Hence, No. of students  required to attend the remedial program are = 0.0179 $\times$ 1200=21.48

So, approx. 22 students are of IQ of 87 and lower than are required to attend the remedial program.