Interactive practice questions
For the average individual, completing their personal income tax return can take between $1$1 and $6$6 hours.
The time taken to complete the tax return, where $t$t is the time in hours, can be modelled by the probability density function:
| $f\left(t\right)$f(t) | $=$= |  |
$k\left(t-1\right)\left(6-t\right)\left(t+2\right)$k(t−1)(6−t)(t+2) | if $1\le t\le6$1≤t≤6 | ||
| $0$0 | for all other values of $t$t |
Calculate the value of $k$k, using the capabilities of your CAS calculator.
Calculate the probability, $p$p, that it takes someone exactly $2$2 hours to complete their tax return.
Using the capabilities of your CAS calculator, calculate the probability, $q$q, that it takes someone between $2$2 and $3.5$3.5 hours to complete their tax return. Give your answer correct to two decimal places.
Let $T$T be the continuous random variable representing the time it takes for an individual to complete their personal income tax return. Use calculus to calculate the expected value of $T$T to two decimal places.
The time $t$t, in hours, that an owl spends hunting each night can be modelled by a continuous random variable with probability density function given below.
The amount of coffee used by a café each week is modelled by a continuous random variable $X$X with a mean of $14.5$14.5 kg and a standard deviation of $1.5$1.5 kg. If the coffee costs $C=24X+15$C=24X+15 in dollars (due to cost per kg and weekly delivery fee), find:
A written French examination is worth a total of $180$180 marks. The results of the examination can be modelled by a continuous random variable $X$X where the expected value $E\left(X\right)$E(X) is $117$117 and the variance $V\left(X\right)$V(X) is $15$15.