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

Question 1

Skill question

Calculate $P (26 < X < 34)$ , given that $X \sim N (30, 4^{2})$ .

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Question 2

Skill question

Let $X$ be a random variable such that $X \sim N (0, 1)$ .

Determine $P (- 1.5 < X < 0.5)$ .

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Question 3

Skill question

The random variable $X$ follows a normal distribution such that $X \sim N (4.5, 1. 5^{2})$ .

Find $P (3 < X < 5)$ .

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Question 4

Skill question

Calculate $P (X > 12)$ for $X \sim N (10, 2^{2})$ .

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Question 5

Skill question

Find $P (X < 15)$ for $X \sim N (20, 5^{2})$ .

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Question 6

Skill question

Find $P (X < 3.6)$ if $X \sim N (5, 0. 8^{2})$ .

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Question 7

Skill question

Compute $P (X > 125)$ for $X \sim N (100, 1 5^{2})$ .

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Question 8

Skill question

If $X \sim N (8, 3^{2})$ , determine the value of $b$ such that $P (X < b) = 0.90$ .

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Question 9

Skill question

For $X \sim N (0, 2)$ , determine $d$ such that $P (- d < X < d) = 0.80$ .

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Question 10

Skill question

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

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Question 11

Skill question

Find $P (40 < X < 60)$ given that $X \sim N (50, 1 0^{2})$ .

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Question 12

Skill question

Let $X$ be a normally distributed random variable such that $X \sim N (100, 2 0^{2})$ .

Find the value of $c$ such that $P (X > c) = 0.05$ .

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IB Mathematics Applications & Interpretation Question Type 3: Finding the Probability Values of Normally Distributed Variables Exercises