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

Question 1

Skill question

Find $a$ for $X \sim N (8, 3^{2})$ such that $P (X < a) = 0.95$ .

[3]

Question 2

Skill question

Determine the value of $a$ if $X \sim N (8, 3^{2})$ and $P (X < a) = 0.90$ .

[3]

Question 3

Skill question

For $X \sim N (50, 1 0^{2})$ , find the value of $a$ such that $P (X < a) = 0.975$ .

[3]

Question 4

Skill question

For $X \sim N (100, 1 5^{2})$ , determine the value of $a$ such that $P (X > a) = 0.05$ .

[4]

Question 5

Skill question

This question requires finding a specific value for a normally distributed random variable given a probability.

For $X \sim N (60, 5^{2})$ , find the value of $a$ such that $P (X > a) = 0.25$ .

[4]

Question 6

Skill question

Find $a$ for $X \sim N (8, 3^{2})$ such that $P (X > a) = 0.95$ .

[4]

Question 7

Skill question

The question concerns finding a specific value in a normal distribution given its cumulative probability.

Find the value of $a$ such that for $X \sim N (8, 3^{2})$ , $P (X < a) = 0.75$ .

[3]

Question 8

Skill question

A random variable $X$ follows a normal distribution such that $X \sim N (8, 3^{2})$ .

Find the value of $a$ such that $P (X > a) = 0.75$ .

[4]

Question 9

Skill question

For $X \sim N (150, 2 0^{2})$ , determine $a$ such that $P (X < a) = 0.05$ .

[3]

Question 10

Skill question

For $X \sim N (8, 3^{2})$ , find $a$ such that $P (X > a) = 0.10$ .

[4]

Question 11

Skill question

Statistics and probability: Normal distribution

Determine $a$ if $X \sim N (8, 3^{2})$ and $P (X > a) = 0.90$ .

[3]

Question 12

Skill question

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

[3]

IB Mathematics Applications & Interpretation Question Type 4: Finding the Value of X Using Inverse Normal Exercises