Question

Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the following conditions. (Round your answers to two decimal places.)
a. P(z < z*) = 0.0244
z* =

b. P(z < z*) = 0.0098
z* =

c. P(z < z*) = 0.0496
z* =

d. P(z > z*) = 0.0204
z* =

e. P(z > z*) = 0.0098
z* =

(f) P(z > z* or z < -z*) = 0.201
z* =

Answer 1

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.

Answer 2

Answer:

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Step-by-step explanation: