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CanadaON
Grade 12

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.

Heights (cm)Relative Frequency (%)5101520253035404550145 -149150-154155-159160-164165-169170-179
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
8min

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

Easy
8min

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

Easy
5min

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

Medium
2min
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Outcomes

12D.B.2.1

Recognize and identify a continuous random variable, and distinguish between situations that give rise to discrete frequency distributions and situations that give rise to continuous frequency distributions

12D.B.2.4

Represent, using intervals, a sample of values of a continuous random variable numerically using a frequency table and graphically using a frequency histogram and a frequency polygon, recognize that the frequency polygon approximates the frequency distribution, and determine, through investigation using technology, and compare the effectiveness of the frequency polygon as an approximation of the frequency distribution for different sizes of the intervals

12D.B.2.5

Recognize that theoretical probability for a continuous random variable is determined over a range of values, that the probability that a continuous random variable takes any single value is zero, and that the probabilities of ranges of values form the probability distribution associated with the random variable

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