Step-by-step explanation:
68% of all values are within 1 SD (110 ± 15).
95% of all values are within 2SD (110 ± 2×15 = 30)
99.7% of all values are within 3 SD (110 ± 3×15 = 45)
a)
95 is 110 - 15, so exactly 1 SD apart from the mean value.
68% or 0.68 is the probability of all values between 95 and 125.
so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 95 is
0.34 + 0.5 = 0.84
b)
125 is 110 + 15, so exactly 1 SD apart from the mean value.
so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.
so, the probability of all values larger than 125 is
0.5 - 0.34 = 0.16
