8.15 Sample means and population means
Interactive practice questions
A random number generator, generates random integers, $X$X, between $43$43 and $65$65 with equal probability.
What type of probability distribution does this scenario represent?
Uniform continuous probability distribution
Uniform discrete probability distribution
What is the mean or expected value of this distribution of generated random numbers?
A sample of $10$10 numbers are generated and shown below.
$43,49,62,57,47,64,58,50,59,47$43,49,62,57,47,64,58,50,59,47
Calculate the mean of this sample data.
A spinner is split into $5$5 equal sections, and these sections are numbered from $1$1 to $5$5. The spinner is used to generated random integers, $X$X, between $1$1 and $5$5 with equal probability.
The position $X$X that a raindrop falls on the interval $\left[0,8\right]$[0,8] in meters is found to be equally likely for all possible $x$x.
In 2016, the mean result of all Western Australian students sitting the Mathematics Methods exam was $58%$58%, with a standard deviation of $15%$15%. A sample of $15$15 students were chosen at random and their results are shown below.
$56.07,49.91,34.32,83.07,57.22,82.88,27.42,65.28,61.43,38.35,70.6,66.46,36.51,67,46.93$56.07,49.91,34.32,83.07,57.22,82.88,27.42,65.28,61.43,38.35,70.6,66.46,36.51,67,46.93