Exercises for Question Type 3: Finding the probability values of normally distributed variables

Question 1

Skill question

Find $P (X > 25)$ for $X \sim N (20, 3^{2})$ .

[2]

Question 2

Skill question

Find $P (X < 2)$ for $X \sim N (5, 2^{2})$ .

[3]

Question 3

Skill question

Find $P (65 < X < 80)$ for $X \sim N (70, 3^{2})$ .

[4]

Question 4

Skill question

Calculate $P (3 < X < 5)$ for $X \sim N (4.5, 1. 5^{2})$ .

[4]

Question 5

Skill question

Find $P (X > 13)$ for $X \sim N (10, 2^{2})$ .

[4]

Question 6

Skill question

Calculate $P (X < 28)$ for $X \sim N (30, 4^{2})$ .

[2]

Question 7

Skill question

Determine $P (230 < X < 260)$ for $X \sim N (250, 1 0^{2})$ .

[2]

Question 8

Skill question

Calculate $P (X > 18)$ for $X \sim N (15, 2. 5^{2})$ .

[2]

Question 9

Skill question

Find $P (45 \leq X \leq 60)$ for $X \sim N (50, 5^{2})$ .

[4]

Question 10

Skill question

Calculate $P (X < 85)$ for $X \sim N (100, 1 5^{2})$ .

[3]

Question 11

Skill question

Compute $P (Z > 2.33)$ for $Z \sim N (0, 1)$ .

[2]

Question 12

Skill question

Determine $P (- 1.96 < Z < 1.96)$ for $Z \sim N (0, 1)$ .

[3]

IB Mathematics Analysis and Approaches Question Type 3: Finding the Probability Values of Normally Distributed Variables Exercises