From a score x we calculate z=(x - μ)/σ and look up the result in the standard normal table.
x=68, z=(68-75)/7 = -1
x=82, z=(82-75)/7 = 1
Nice, we don't have to look anything up. By the 68-95-99.7 rule 68% of the scores fall between plus or minus one standard deviation from the mean.
a) Answer: 68%
x=54, z=(54-75)/7 = -3
x = 96, z=(96-75)/7 = 3
Same rule, plus or minus three sigma gives 99.7% of the scores
b) Answer: 99.7%
