Random Variables New Zealand
Level 7 - NCEA Level 2

Continuous Random Variable

Interactive practice questions

The data given shows the heights of a group of $16$16 year-olds to the nearest cm.

Heights (cm)
$148,161,154,160,150,153,155,158,156,168,147,157,153,165,148,162,164,163,154,154$148,161,154,160,150,153,155,158,156,168,147,157,153,165,148,162,164,163,154,154
a

Complete the following relative frequency table

Height Frequency Relative Frequency
$145\le h<150$145h<150 $\editable{}$ $\editable{}$
$150\le h<155$150h<155 $\editable{}$ $\editable{}$
$155\le h<160$155h<160 $\editable{}$ $\editable{}$
$160\le h<165$160h<165 $\editable{}$ $\editable{}$
$165\le h<170$165h<170 $\editable{}$ $\editable{}$
$170\le h<175$170h<175 $\editable{}$ $\editable{}$
b

Use the table from part (a) to make a relative frequency histogram.

c

Use your relative frequencies to calculate the probability of a student being between $155$155 and $159$159 cm tall, inclusive.

d

Use your relative frequencies to calculate the probability of a student being less than $155$155 cm.

Easy
Approx 9 minutes

The data below shows the time spent waiting for a green light at a set of traffic lights, in seconds.

The IQ test results for $50$50 people aged $30$30 is represented by the relative frequency histogram below.

The average time ($t$t), in seconds, between $50$50 customers filling up their cars at a petrol station on a Monday morning between $8$8am and $10$10am is given in the relative frequency histogram below.

Outcomes

S7-4

S7-4 Investigate situations that involve elements of chance: A comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions B calculating probabilities, using such tools as two-way tables, tree diagrams, simulations, and technology.

91267

Apply probability methods in solving problems