Exercises for Question Type 4: Finding the value of X using inverse normal

Question 1

Skill question

For $X \sim N (8, 3^{2})$ , find the value $a$ such that $P (X > a) = 0.75$ .

[4]

Question 2

Skill question

For $Z \sim N (0, 1)$ , find $z$ such that $P (Z > z) = 0.1587$ .

[2]

Question 3

Skill question

Test scores $X \sim N (70, 8^{2})$ . Find the pass mark $p$ so that only the top $10%$ of students pass.

[3]

Question 4

Skill question

For $X \sim N (60, 1 2^{2})$ , find $g$ such that $P (g < X < 75) = 0.80$ .

[5]

Question 5

Skill question

For $X \sim N (120, 1 5^{2})$ , find $k$ such that $P (X < k) = 0.025$ .

[2]

Question 6

Skill question

Lifetimes of bulbs $X \sim N (2000, 20 0^{2})$ . Find the lifetime $L$ below which $30%$ of bulbs fail.

[3]

Question 7

Skill question

Let $Z \sim N (0, 1)$ . Find $z$ such that $P (- z < Z < z) = 0.95$ .

[2]

Question 8

Skill question

For $X \sim N (100, 1 0^{2})$ , find $c$ such that $P (X > c) = 0.05$ .

[3]

Question 9

Skill question

For $X \sim N (5, 2^{2})$ , find values $a$ and $b$ symmetric about the mean so that $P (a < X < b) = 0.80$ .

[4]

Question 10

Skill question

For $X \sim N (8, 3^{2})$ , find $b$ such that $P (X < b) = 0.60$ .

[4]

Question 11

Skill question

For $X \sim N (20, 4^{2})$ , find $f$ such that $P (X > f) = 0.20$ .

[4]

IB Mathematics Analysis and Approaches Question Type 4: Finding the Value of X Using Inverse Normal Exercises