Answer: 35
Step-by-step explanation:
Given : The IQs of 700 applicants to a certain college are approximately normally distributed with a mean of 115 and a standard deviation of 11.
i.e. [tex]\mu=115[/tex] and [tex]\sigma= 11[/tex]
Let x denotes the IQs of applicants to college.
If the college requires an IQ of at least 97, then, the probability that students have IQ less than 97:-
[tex]P(x<97)=P(\dfrac{x-\mu}{\sigma}<\dfrac{97-115}{11})\\\\=P(z<-1.64) = 1-P(z<1.64)\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=1-0.9495=0.0505[/tex] [By using z-table]
Number of students will be rejected on this basis of IQ = Total students x Probability of students have IQ less than 97
= 700 x 0.0505 = 35.35 ≈ 35
Hence, about 35 students will be rejected on this basis of IQ, regardless of their other qualifications .
