Question

Determine the value z* that satisfies the conditions below. (Round all answers to two decimal places.) (a) Separates the largest 3% of all z values from the others z* = 1.81 Incorrect: Your answer is incorrect. (b) Separates the largest 1% of all z values from the others z* = 2.33 Correct: Your answer is correct. (c) Separates the smallest 4% of all z values from the others z* = 1.76 Incorrect: Your answer is incorrect. (d) Separates the smallest 10% of all z values from the others z* = 1.29 Incorrect: Your answer is incorrect.

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The z score is used to determine by how many standard deviations the raw sore is above or below the mean.

a) For the largest of 3%:

P(z > z*) = 3%

P(z > z*) = 0.03

P(z > z*) = 1 - P(z < z*)

1 - P(z < z*) =  0.03

P(z < z*) = 1 - 0.03

P(z < z*) = 0.97

The z score that corresponds with 0.97 is 1.88. Hence:

z* = 1.88

b)  For the largest of 1%:

P(z > z*) = 1%

P(z > z*) = 0.01

P(z > z*) = 1 - P(z < z*)

1 - P(z < z*) =  0.01

P(z < z*) = 1 - 0.01

P(z < z*) = 0.99

The z score that corresponds with 0.99 is 2.33. Hence:

z* = 2.33

c)  For the smallest of 4%:

P(z < z*) = 0.04

The z score that corresponds with 0.04 is -2.65. Hence:

z* = -2.65

d)  For the smallest of 10%:

P(z < z*) = 0.1

The z score that corresponds with 0.1 is -1.28. Hence:

z* = -1.28