$2.($a$)$ State whether each of the following is a$)$ Qualitative $-$ ordinal, b$)$ Qualitative

$-$ nominal, c$)$ Quantitative $-$ continuous or d$)$ Quantitative $-$ discrete:

$($i$)$ Wait time in the Accident and Emergency $($A & E$)$ department $[1]$

$($ii$)$ Marital status $($single$,$ married, divorced etc.$)[1]$

$($iii$)$ Star rankings $($Bronze$,$ Silver, Gold, and Platinum$)[1]$

$($iv$)$ Number of infrastructure projects $($e$.$g$.,$ new roads, bridges$)[1]$

$($b$)$ State two approaches for deciding whether data is skewed. $[4]$

$($c$)$ Events A and B in a sample space satisfy P$($A$)=0\mathrm{.}6,$ P$($B$)=0\mathrm{.}2$ and P$($A$\backslash$cap B$)$

$=0\mathrm{.}12.$ Are these two events mutually exclusive $($disjoint$)?$ Are these two

events independent? $[6]$

$($d$)$ According to the Sustainable Energy Authority Of Ireland, there were a total

of $105,253$ new car registrations in $2022($assume no more than one car was

bought per household$).$ This included $62,157$ petrol$/$diesel cars, and $43,096$

electric$/$hybrid cars. A recent survey has found that $78\%$ of electric$/$hybrid

car owners have a home car$-$charger and $0\mathrm{.}8\%$ of petrol$/$diesel car owners have

a home car charger.

Based on the $2022$ car registration information:

$($i$)$ Calculate the probability of having a home car charger. $[6]$

$($ii$)$ If a car owner has a home charger, what is the probability of them owning

an electric$/$hybrid car? $[5]$

$($iii$)$ If a car owner has a home charger, what is the probability of them owning

a petrol$/$diesel car?