Problem 1012pts) The scores on the entrance exam for a very exclusive university

Question

Problem 1012pts) The scores on the entrance exam for a very exclusive university program are normaly dstributed with a mean score of 60 and a standard deviation equal to 15. a) What proportion of all students taking the exam receive a score of less than 70 points? Show your work and give your answer rondeduRibeneamst1decimaldigt pts) b) What proportion of al students taking the exam receive a score between 30 and 90 points? Show pts) your work and give your answer c) the university sets the bar at 85 pts to beadmited what proportion of applicants are admitted? pts) Show your work and give your answer

Explanation / Answer

Problem - 1:

a) P(X < 70)

= P(z < (70 - 60)/15)

= P(z < 0.67)

= 0.748

So,

The proportion of students receiving the score less than 70 is 74.8%.

b) P(30 < X < 90)

= P((30 - 60)/15 < z < (90 - 60)/15)

= P(-2 < z < 2)

= 0.954

Hence,

The proportion of students scored between 30 and 90 points is 95.4%.

c) P(X > 85)

= P(z > (85 - 60)/15)

= P(z > 1.67)

= 0.048

Hence,

The proportion of students who got admitted is 4.8%.

d) From z table,

P(z > 2.33) = 0.01

Hence,

Lowest passing score = 60 + 2.33(15) = 94.95 = 95 (Rounded off to the nearest unit)

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