Mathematics Methods · Unit 4 · Topic 4.2

Continuous random variables and the normal distribution

5 free questions, 4 calculator-free and 1 calculator-assumed, with worked solutions written like marking keys.

Calculator-assumedstandard

A continuous random variable has probability density function

f(x) = \frac{x}{8}

for

0 \le x \le 4

. Determine

P(X < 2)

4 marks

Calculator-freefoundation

For

X \sim N(10, 2^2)

, determine the

z

-score of

x = 13

2 marks

Calculator-freefoundation

A continuous random variable is uniformly distributed on

0 \le x \le 5

, so

f(x) = \frac{1}{5}

. Determine

P(X < 2)

3 marks

Calculator-freefoundation

In a sample of

250

measurements,

30

fall in a particular interval. Estimate the probability that a measurement falls in that interval.

2 marks

Calculator-freefoundation

For

X \sim N(60, 8^2)

, determine the

z

-score of

x = 48

2 marks