Assume a data set is normally distributed with mean 182 and standard deviation 30. If the data set contains 600 data values, approximately how many of the data values will fall within the range 122 to 242?

Answer 1

122
z = (122-182)/30 = -2

242
z = (242 - 182)/30 = +2

then use normal table

or use:
for example
http://davidmlane.com/hyperstat/z_table.html

result .9545 in that range so
.9545*600 = 573