I believe the parts are:
A. What is the probability that Upper X greater than
95X>95?
B. What is the probability that Upper X less than
75X<75?
C.What is the probability that Upper X less than
85X<85 and Upper X greater than 125X>125?
D. 95% of the values are between what two X-values
(symmetrically distributed around the mean)?
<u>Solution:</u>
We use the equation for z score:
z = (X – μ) / σ
Then use the standard normal
probability tables to locate for the value of P at indicated z score value.
A. Z = (95 – 100) / 10 = -
0.5
Using the tables, the
probability at z = -0.5 using right tailed test is:
P = 0.6915
B. Z = (75 – 100) / 10 = -
2.5
Using the tables, the
probability at z = -2.5 using left tailed test is:
P = 0.0062
C. Z = (85 – 100) / 10 = -
1.5
Using the tables, the
probability at z = -2.5 using left tailed test is:
P = 0.0668
Z = (125 – 100) / 10 = 2.5
Using the tables, the
probability at z = 2.5 using right tailed test is:
P = 0.0062
So the probability that
85<X and X>125 is:
P(total) = 0.0668 + 0.0062
P(total) = 0.073
D. P(left) = 0.025, Z =
-1.96
P(right) = 0.975, Z = 1.96
The X’s are calculated
using the formula:
X = σz + μ
At Z = -1.96
X = 10 (-1.96) + 100 =
80.4
At Z = 1.96
X = 10 (1.96) + 100 =
119.6
<span>So 95% of the values are
between 80.4 and 119.6 (80.4< X <119.6).</span>
