Population and Sampling Distribution

Question

For a normal distribution that has a mean of 100 and a standard deviation of 8.  Determine the Z-score for each of the following X values:

X = 108	Z =
X = 112	Z =
X = 98	Z =
X = 70	Z =
X = 124	Z =
Use the information in 1 A to determine the area or probability of the following:
p(x > 108)
p(x < 98)
p(92 < x < 108)
p(84 < x < 116)
p(x < 84)

Answer 1

X	Z=(X-100)/8	N(Z)
70	-3.75	1-0.9999=0.0001
84	-2	1-0.9772=0.0228
92	-1	1-0.8413=0.1587
98	-0.25	1-0.5987=0.4013
108	1	0.8413
112	1.5	0.9332
116	2	0.9772
124	3	0.9987

The diagrams (not to scale) below symbolically explain the arithmetic.

P(X>108)=1-0.8413=0.1587

P(X<98)=0.4013

P(92<X<108)=0.8413-0.1587=0.6826

P(84<X<116)=0.9772-0.0228=0.9544

P(X<84)=0.0228