The distribution of the SAT scores in mth for an incoming class of business stud

Question

The distribution of the SAT scores in mth for an incoming class of business students has a mean of 590 and standard deviation of 22. Assume that scores are normally distributed.

A) Fimd the probability that a student's SAT score is less than 550.

B) Find the probability that an individual's SAT score is between 550 and 600.

C) Find the probability that individual's SAT score is greater than 620.

D) What percentage of students will have scored better than 700?

E) Find the standardization values for students scoring 550, 600, 650, and 700 on their test.

Explanation / Answer

Normal Distribution
Mean ( u ) =590
Standard Deviation ( sd )=22
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 550) = (550-590)/22
= -40/22= -1.8182
= P ( Z <-1.8182) From Standard Normal Table
= 0.0345                  

b)                  
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 550) = (550-590)/22
= -40/22 = -1.8182
= P ( Z <-1.8182) From Standard Normal Table
= 0.03452
P(X < 600) = (600-590)/22
= 10/22 = 0.4545
= P ( Z <0.4545) From Standard Normal Table
= 0.67528
P(550 < X < 600) = 0.67528-0.03452 = 0.6408                  

c)
P(X > 620) = (620-590)/22
= 30/22 = 1.3636
= P ( Z >1.364) From Standard Normal Table
= 0.0863

d)
P(X > 700) = (700-590)/22
= 110/22 = 5
= P ( Z >5) From Standard Normal Table
= 0                  
Zero pertange of students scored better than 700

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