Please help with a statistics question.

Question

THE MEAN TOTAL CHOLESTEROL FOR A POPULATION OF MEN BETWEEN THE AGES OF 20 AND 29 IS
180 MICROGRAMS PER DECILITER WITH A STANDARD DEVIATION OF 34.8. A HEALTHY TOTAL
CHOLESTEROL LEVEL IS LESS THAN 200, 200-240 IS BORDERLINE, AND ABOVE 240 IS DANGEROUS.
ASSUME THAT THE DISTRIBUTION IS NORMAL TO ANSWER THE FOLLOWING:

A. FOR A RANDOMLY SELECTED MAN FROM THIS GROUP, WHAT IS THE
PROBABILITY THAT HIS TOTAL CHOLESTEROL LEVEL IS 200 OR MORE?

 

B. FOR A RANDOMLY SELECTED MAN FROM THIS GROUP, WHAT IS THE
PROBABILITY THAT HIS TOTAL CHOLESTEROL LEVEL IS 240 OR MORE?

 

C. WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED MAN HAS A
BORDERLINE CHOLESTEROL LEVEL?

 

D. WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED MAN HAS A HEALTHY
CHOLESTEROL LEVEL?

 

E. IF 700 RANDOMLY SELECTED MEN ARE CHOSEN FROM THIS GROUP, HOW
MANY (COUNT, NOT PERCENTAGE) WOULD YOU EXPECT TO HAVE A TOTAL
CHOLESTEROL LEVEL OF 200 OR MORE?

Answer 1

(A) If the mean is 180 and s.d. is 34.8 you would use the transformation z=(200-180)/34.8.

 

Then look this up in the normal table:

 

https://www.wyzant.com/resources/files/392716/normal_dist_table/download?encryptedID=uMpgXg5183c%3D&d=v

 

Subtract the value you get from the table from .5 to get the answer.

 

 

Any questions on how to do this step?