The scores on a standardized mathematics test for 8th-grade children in New York State form a normal
distribution with a mean of µ ! 70 and a standard
deviation of $ ! 10.
a. What proportion of the students in the state have
scores less than X ! 75?
b. If samples of n ! 4 are selected from the
population, what proportion of the samples will
have means less than M ! 75?
c. If samples of n ! 25 are selected from the
population, what proportion of the samples will
have means less than M ! 75?