Answer:
a) z* = -1.97
b) z* = -2.33
c) z* = -1.65
d) z* = 2.04
e) z* = 2.33
f) z* = -1.25.
Step-by-step explanation:
Z-score:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
a. P(z < z*) = 0.0244
We have to look at the ztable, and find z which has a pvalue of 0.0244. So it is z* = -1.97
b. P(z < z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 0.0098. So it is z* = -2.33
c. P(z < z*) = 0.0496
We have to look at the ztable, and find z which has a pvalue of 0.0496. So it is z* = -1.65
d. P(z > z*) = 0.0204
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0204 = 0.9796. So z* = 2.04
e. P(z > z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0098 = 0.9902. So z* = 2.33
(f) P(z > z* or z < -z*) = 0.201
This is z which has a pvalue of 0.201/2 = 0.1055. So it is z* = -1.25.
