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