Question

All applicants at a large university are required to take a special entrance exam before they are admitted. The exam scores are known to be normally distributed with a mean of 300 and a standard deviation of 70. Applicants must score 230 or more on the exam before they are admitted. (a) What proportion of all applicants taking the exam is granted admission? (Round your answer to four decimal places.) (b) What proportion of all applicants will score 440 or higher on the exam? (Round your answer to four decimal places.) (c) For the coming academic year, 2400 applicants have registered to take the exam. How many do we expect to be qualified for admission to the university? (Round your answer to the nearest whole number.)

Answer 1

Answer:

Step-by-step explanation:

Let X be the exam scores of all applicants at a large university

X is given to be N(300, 70)

Applicants must score 230 or more on the exam before they are admitted

i.e. proportion of all applicants taking the exam is granted admission

= $P(X\geq 230)\\= 0.841345$

=0.8413

Nearly 84.13% of applicants applied are granted admission.

b) proportion of all applicants will score 440 or higher on the exam

=$P(X\geq 440)\\=0.02275\\=0.0228$

c) No of applicants = 2400

Admission to the university =0.8413 *2400

= 2019.12

2019