Interactive practice questions
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.
| $f\left(t\right)$f(t) | $=$= |  |
$\frac{k}{32}t\left(4-t\right)$k32t(4−t), $0\le t\le4$0≤t≤4 |
| $0$0 otherwise |
Determine the value of $k$k.
Calculate the probability the owl spends more than $3$3 hours hunting during one night.
Calculate the expected time the owl spends hunting in hours.
Calculate the standard deviation of the time the owl spends hunting in hours.
Round your answer to two decimal places.
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.
An artist taking commissions on cartoons takes between $2$2 and $5$5 hours to complete pieces. The time varies and can be approximately modelled by the following probability density function.