NZ Level 7 (NZC) Level 2 (NCEA)

Continuous Random Variable

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$145≤h<150 |
$\editable{}$ | $\editable{}$ |

$150\le h<155$150≤h<155 |
$\editable{}$ | $\editable{}$ |

$155\le h<160$155≤h<160 |
$\editable{}$ | $\editable{}$ |

$160\le h<165$160≤h<165 |
$\editable{}$ | $\editable{}$ |

$165\le h<170$165≤h<170 |
$\editable{}$ | $\editable{}$ |

$170\le h<175$170≤h<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

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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.

Apply probability methods in solving problems