Homework SourseThe average score on the SSC303 exam is u70 and the standard
The average score on the SSC303 exam is u=70 and the standard deviation is 4. A) what is the probability that a student will score between 72 and 80? B) what is the probability that a student will score 65? C) what is the probability that a student will score more than 75? D) what should a student score to be on the top 10%?
The average score on the SSC303 exam is u=70 and the standard deviation is 4. A) what is the probability that a student will score between 72 and 80? B) what is the probability that a student will score 65? C) what is the probability that a student will score more than 75? D) what should a student score to be on the top 10%?
Solution
mu =70
Let x be the score.
X is normal (70,4)
A) Prob (a student will score between 72 and 80)
= P(72<x<80)
= P(0.5<z<2.5)
=0.4938-0.1915
= 0.3023
B) probability that a student will score 65
= P(X=65)
=0 as in a continuous distribution for a particular value prob =0
C) probability that a student will score more than 75
= P(X>75) =P(Z>1.25) = 0.5-0.3944
= 0.1056
D) a student score to be on the top 10%?
P(Z>z) =0.10
z = 1.28
x = 70+1.28(4)
= 70+5.12
= 75.12
