RevisionDojo

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

Question 1

Calculate $P(X > 5)$ for $X \sim N(2, 4)$ .

[3]

Question 2

Let $X \sim N(2, \sigma^2)$ and $P(X > a) = 0.3$ . Find $1 - P(X < 4 - a)$ .

[3]

Question 3

For $X \sim N(8, \sigma^2)$ , if 95% of the data lies between 6.5 and 9.5, find the value of $\sigma^2$ .

[4]

Question 4

The use of a graphic display calculator (GDC) is expected for finding normal distribution values.

A test score is modeled by a normal distribution $X \sim N(100, \sigma^2)$ . Given that 80% of students score between 90 and 110, find the value of $\sigma^2$ .

[4]

Question 5

The random variable $X$ follows a normal distribution with mean $\mu = 0$ and variance $\sigma^2 = 9$ . Find the probability that $X$ lies within the interval $[-1, 2]$ .

Calculate $P(-1 \le X \le 2)$ for $X \sim N(0,9)$ .

[4]

Question 6

For $X \sim N(3, 16)$ , show that $P(X < -1) = P(X > 7)$ and compute this probability.

[5]

Question 7

Mathematics: analysis and approaches

Let $X \sim N(2, \sigma^2)$ and $P(X > a) = 0.3$ . Express $a$ in terms of $\sigma$ .

[3]

Question 8

Calculate $P(X < 1.96)$ for $X \sim N(0,1)$ .

[2]

Question 9

For $X \sim N(0, \sigma^2)$ , if 95% of the data lies between $-3$ and $3$ , find $\sigma$ .

[2]

Question 10

For $X \sim N(10, \sigma^2)$ , the central $90\%$ of the data lies between 8 and 12. Find the value of $\sigma$ .

[3]

Question 11

This question assesses the ability to use the standard normal distribution and symmetry to find an unknown parameter of a normal distribution.

Let $X \sim N(5, \sigma^2)$ . Given that $99\%$ of the data lies between $3$ and $7$ , find the value of $\sigma$ .

[4]

Question 12

For $X \sim N(20, \sigma^2)$ , the interval $[10, 30]$ contains $95\%$ of the values. Find $\sigma^2$ .

[3]

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