Question

lucy got a score of 75 from her stats class. Assuming the scores of her class formed a normal distribution and had a mean of 60 and a standard deviation of 5. a. What is Lucys percentile rank? b. How would you explain her percentile rank to your grandmother? c.Lucy's history class also has a normal distribution on the first test(M=70, S=10) and her score was 75 too. What class did she do relatively better or do you think she did equally well in both classes? Briefly explain

Answer 1

Solution:

Given :Lucy got a score of 75 from her stats class. Assuming the scores of her class formed a normal distribution and had a mean of 60 and a standard deviation of 5

x = 75

Part a) What is Lucys percentile rank?

P( X < 75 ) = ......?

Find z score:

Thus we get:

P( X < 75) = P( Z < 3.00)

Look in z table for z = 3.0 and 0.00 and find area , which gives : P( Z < 3.00) = 0.9987

That is: P( X < 75) = 0.9987 = 99.87%

thus Lucy's percentile rank = 99.87%

Part b) How would you explain her percentile rank to your grandmother?

Lucy's percentile rank = 99.87% , which means 99.87% of the other students are below Lucy's score.

Part c.Lucy's history class also has a normal distribution on the first test(M=70, S=10) and her score was 75 too. What class did she do relatively better or do you think she did equally well in both classes? Briefly explain

x= 75

Find P( X < 75) = ....?

Thus we get:

P(X < 75) =P( Z < 0.50)

Look in z table for z = 0.5 and 0.00 and find area, which gives P(Z < 0.50)= 0.6915

Thus

P( X < 75) = 0.6915 = 69.15%

Since for Stats class percentile rank is 99.87% , whereas for History , its 69.15%

Hence she did relatively better in Stats class.