$($More practice on the binary operators$)$ Prof. Lee is taking his friends and family to La Ronde, Montreal$$s iconic amusement park. The heights of his group of $10$ people, measured in centimeters, are recorded in the following vector:

heights $=$ c$(145\mathrm{.}5,189\mathrm{.}7,183,135\mathrm{.}3,175,178,162,102,168\mathrm{.}8,195\mathrm{.}2)$

Prof. Lee$$s group is eager to ride the roller coaster, but there$$s a catch: only those whose height falls between $150$ cm and $185$ cm are allowed on the ride. With this heartbreaking news, answer the following questions:

To quickly determine who meets the height requirement, Prof. Lee decides to assign each person a unique English letter. In R$,$ the LETTERS vector provides all the capital letters of the alphabet.

LETTERS

$[1]"$A$""$B$""$C$""$D$""$E$""$F$""$G$""$H$"$ "I" $"$J$""$K$""$L$""$M$""$N$""$O$""$P$""$Q$""$R$""$S$"$

$[20]"$T$""$U$""$V$""$W$""$X$""$Y$""$Z$"$

Using LETTERS, find a simple way to assign $"$A$"$ to $"$J$"($in order$)$ to each member of the group. So you$$ll have to have the following:

heights

A B C D E F G H I J

$145\mathrm{.}5189\mathrm{.}7183\mathrm{.}0135\mathrm{.}3175\mathrm{.}0178\mathrm{.}0162\mathrm{.}0102\mathrm{.}0168\mathrm{.}8195\mathrm{.}2$

NOTE. Refrain from manually assigning characters to the group members one$-$by$-$one.

Next, we need to determine who is too tall, too short, or appropriately sized for the ride. Using appropriate binary operators, create a new vector named heights$\_$eval. This vector should have the same indices as heights, with values assigned according to the following rules:

If the height is less than $150,$ assign $$short$.$

If the height is between $150$ and $185($inclusive$),$ assign $$pass$.$

If the height is greater than $185,$ assign $$tall$.$

The resulting vector should look like this:

heights$\_$eval

$[1]$ "short" "tall" "tall" "short" "pass" "pass" "pass" "short" "pass"

$[10]$ "tall"

Hint. You can start creating a vector of length $10$ and modify the values later. For example, heights$\_$eval $=$ rep$(0,10)$ does the job.

By using the results from part $($a$)$ and $($b$),$ write a code that prints the names whose height is appropriate for the ride. So your code should print the following:

$[1]"$E$""$F$""$G$"$ "I"

Instead of riding the roller coaster, Prof. Lee$$s group decided to try a different attraction. Fortunately, everyone can take this ride, but the entrance fee varies based on height:

Heights below $150$ cm: $3$ CAD

Heights between $150$ and $185$ cm $($inclusive$)$: $4$ CAD

Heights above $185$ cm: $5$ CAD

Using your solutions from parts $($a$)$ and $($b$),$ write a code that calculates and prints the total entrance fee Prof. Lee$$s group has to pay.

$[1]40$

NOTE. Refrain from manually assigning entrance fee to the group members one$-$by$-$one.