Exercises for Question Type 2: Finding the p-value or critical value given the other for a specific distribution - IB | RevisionDojo

IB
Question Type 2: Finding the p-value or critical value given the other for a specific distribution

Question Type 2: Finding the p-value or critical value given the other for a specific distribution Exercises

Question 1

For $X \sim N(5, 9)$ , calculate the p-value for observing $X \ge 11$ .

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Question 2

For $X \sim N(5, 9)$ , calculate the p-value for observing $X > 8$ .

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Question 3

For $X \sim N(5, 9)$ , find the value $a$ such that $P(X > a) = 0.07$ .

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Question 4

For $X \sim N(5, 9)$ , find $c > 0$ such that $P(|X - 5| > c) = 0.07$ .

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Question 5

Calculating probabilities for a normal distribution.

For $X \sim N(5, 9)$ , calculate the $p$ -value for observing $X < 2$ .

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Question 6

For $X \sim N(5, 9)$ , find the critical value $c$ such that $P(X \ge c) = 0.01$ .

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Question 7

For $X \sim N(5, 9)$ , find $c > 0$ such that $P\bigl(|X - 5| < c\bigr) = 0.93$ .

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Question 8

For $X \sim N(5, 9)$ , find the critical value $a$ such that $P(X < a) = 0.07$ .

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Question 9

For $X \sim N(5, 9)$ , find the critical value $c$ such that $P(X \le c) = 0.025$ .

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Question 10

For $X \sim N(5, 9)$ , given an observed value $x_0 = 10$ , calculate the two-sided $p$ -value for testing $H_0: \mu = 5$ .

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Question 11

For $X \sim N(5, 9)$ , calculate the $p$ -value for observing $X \le -1$ .

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Question 12

Given that $X \sim N(5, 9)$ , calculate $P(2 \le X \le 8)$ .

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