Candace and Stacy are applying to summer school programs Sta

Candace and Stacy are applying to summer school programs. Stacy is applying to a pre-med program, while Candace is applying to a \"learn to bust your brothers\" program. Both programs require an entrance test and both tests are normally distributed. Stacy\'s test has a mean of 25 and a standard deviation of 7. She got a score of 44. Candace\'s test has a mean of 400 and a standard deviation of 120. She got a score of 590. Within their respective groups, who did better?

Stacy did better

Candace did better

They are the same

Solution

Stacy\'s Performence
Mean ( u ) =25
Standard Deviation ( sd )=7
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 44) = (44-25)/7
= 19/7= 2.7143
= P ( Z <2.7143) From Standard Normal Table
= 0.9967                  

Stacy\'s scores almost 99.67% percentile

Candace\'s Performence
Mean ( u ) =400
Standard Deviation ( sd )=120
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 590) = (590-400)/120
= 190/120= 1.5833
= P ( Z <1.5833) From Standard Normal Table
= 0.9433                  

Candace\'s scores almost 95% percentile

We conclude that Stacy did better