Question

Math SAT scores are known to be normally distributed with mean of
500 and standard deviation of 100. Answer the following questions. (I also want to see
good notation and some of your calculations.)
a) Suppose we randomly select one person who has taken the SAT. What is the
probability their math score is between 525 and 550?
b) Suppose we randomly select 25 people who have taken the SAT. What is the
probability their average math score is between 525 and 550?

Answer 1

(a)

= 500

= 100

To find P(525 < X< 550):

For X = 525:

Z = (525 - 500)/100

= 0.25

By Technology, Cumulative Area Under Standard Normal Curve = 0.5987

For X = 550

Z = (550 - 500)/100

= 0.50

By Technology, Cumulative Area Under Standard Normal Curve = 0.6914

So,

P(525 < X< 550):= 0.6914 - 0.5987

                          = 0.0927

So,

Answer is:

0.0927

(b)

= 500

= 100

n = 25

SE = /

= 100/

= 20

To find P(525 < < 550):

For = 525:

Z = (525 - 500)/20

= 1.25

By Technology, Cumulative Area Under Standard Normal Curve = 0.8944

For = 550

Z = (550 - 500)/20

= 2.50

By Technology, Cumulative Area Under Standard Normal Curve = 0.9938

So,

P(525 < < 550):= 0.9938 - 0.8944

                          = 0.0994

So,

Answer is:

0.0994