Exercises for Question Type 1: Using properties of normal distribution to find probabilities given some value

Question 1

Skill question

Let $X \sim N (0, 1)$ . Find the value of $a$ such that $P (X > a) = 0.3$ .

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Question 2

Skill question

Let $X \sim N (0, 1)$ . Given $P (X < a) = 0.05$ , find $P (X > - a)$ .

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Question 3

Skill question

Let $X \sim N (0, 1)$ . Compute $P (∣ X ∣ > 2)$ .

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Question 4

Skill question

Let $X \sim N (2, 4)$ . Find the value $a$ such that $P (X > a) = 0.3$ .

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Question 5

Skill question

Let $X \sim N (5, 16)$ . Find $a$ such that $P (X > a) = 0.025$ .

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Question 6

Skill question

In a population of adult heights, $X \sim N (170, 6^{2})$ . What is the probability that a randomly chosen adult is taller than 172 cm?

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Question 7

Skill question

Let $X \sim N (50, 16)$ . Find $a$ such that $P (X > a) = 0.84$ .

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Question 8

Skill question

Let $X \sim N (100, 25)$ . If $P (X > a) = 0.1$ , find $P (X < 200 - a)$ .

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Question 9

Skill question

Let $X \sim N (3, 1)$ . If $P (X > a) = 0.3$ , calculate $1 - P (X < 4 - a)$ .

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Question 10

Skill question

Let $X \sim N (10, 4)$ . Find $c$ such that $P (10 - c < X < 10 + c) = 0.95$ .

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Question 11

Skill question

Let $X \sim N (10, 9)$ . Find the value $a$ such that $P (X < a) = 0.8$ .

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Question 12

Skill question

Let $X \sim N (0, 1)$ . Given $P (X > 1.3) = p$ , express $P (X < - 1.3)$ in terms of $p$ .

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IB Mathematics Analysis and Approaches Question Type 1: Using Properties of Normal Distribution to Find Probabilities Given Some Value Exercises