5 Use the normal distribution of SAT writing scores with mea

5. Use the normal distribution of SAT writing scores with mean = 493 and standard deviation = 111. a. What percentage of SAT writing scores are less than 600? b. If 1000 SAT writing scores are randomly selected, about how many would you expect to be greater than 550?

Solution

Normal Distribution
Mean ( u ) =493
Standard Deviation ( sd )=111
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 600) = (600-493)/111
= 107/111= 0.964
= P ( Z <0.964) From Standard Normal Table
= 0.8325                  

b)
For sample size( n ) = 1000
Mean ( u ) =493
Standard Deviation ( sd )=111/ Sqrt ( 1000 ) = 3.51
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  

P(X > 550) = (550-493)/111/ Sqrt ( 1000 )
= 57/3.51= 16.2387
= P ( Z >16.2387) From Standard Normal Table
= 0