International Business: The Swiss Franc $($CHF$)$ is the currency and legal tender of Switzerland and Liechtenstein. USD$/$CHF is one of the world's most popular currency pairs to trade and there is a very strong and consistent global demand for both currencies. As such, there is significant liquidity available when trading USD$/$CHF$,$ meaning that you can pretty much trade in real$-$time without any need to wait.

The US dollar, as the world's de facto global reserve currency and the currency in which the majority of foreign debt is held, is a central currency in virtually every aspect of foreign exchange trading. Meanwhile, the Swiss Franc is the world's $8$th most widely held reserve currency and the official currency of one of the most important global epicenters of banking and finance.

The USD$/$CHF currency pair describes the current exchange rate between the US dollar and the Swiss Franc. More specifically, USD$/$CHF indicates how many Swiss Francs it costs to purchase a single US dollar on the global marketplace. For example, if USD$/$CHF is trading at $0\mathrm{.}92,$ then it costs $0\mathrm{.}92$ Francs to buy one dollar. In this case, the Swiss Franc is stronger than the dollar $($A currency is classified as strong when it is worth more than another country's currency$).$ On the other hand, if USD$/$CHF is trading at $1\mathrm{.}12,$ for example, then it costs $1\mathrm{.}12$ Francs to buy one dollar. In this case, the Swiss $.$ Franc is weaker than the dollar.

The USD$/$CHF daily closing rates for the last five years follow a normal distribution with a mean of $0\mathrm{.}81$ points and a standard deviation of $0\mathrm{.}27$ points.

$($a$)$ What does independence mean in a statistical sense in the context of a probability experiment? $($Select all that apply.$)$

The outcome of one trial does not influence the outcome of another trial.

The occurrence of one outcome does not determine the occurrence of another outcome.

The occurrence of one outcome precludes the occurrence of another outcome.

Two events are independent if knowing one event occurred means that the other event cannot occur:

The probability of both trials occurring at the same time is zero.

Two events a $1$ independent if knowing one event occurred doesn't change the probability of the other event.

Do you think that USD$/$CHF closing rates are independent? Why or why not? $($Select all that apply.$)$

Because trading days are independent and disjoint.

Do you think that USD$/$CHF closing rates are independent? Why or why not? $($Select all that apply.$)$

Because trading days are independent and disjoint.

Because these data can be thought of as a time series and times series data are most often correlated through time.

Because these data can be thought of as cross$-$sectional and cross$-$sectional data are collected at a single time point.

No

Yes

Because on any given day, trading begins at the closing rate of the previous day.

$,$ proceed with this analysis assuming that independence is NOT an issue.

$($b$)$ What proportion of USD$/$CHF closing rates are below $0\mathrm{.}49$ points? $($Round your answer to four decimal places$)$

All other things being equal $($which is a BIG assumption in this context$),$ how many closing rates should we expect to be below $0\mathrm{.}49$ points in the next $30$ day period? $($Round your answer to two decimal places$)$

$($c$)$ What is the probability that the USD$/$CHF closing rate for any given day is greater than $0\mathrm{.}32$ points? $($Round your answer to four decimal places$)$

All other things being equal $($which is a BIG assumption in this context$),$ how many closing rates should we expect to be greater than $0\mathrm{.}32$ points in the next $90$ day period? $($Round your answer to two decimal places$)$

$($d$)$ The middle $50\%$ of the closing rates fall between: $($Round your answers to two decimal places$)$

and

$($Enter the lower value first.$)$

What is the IQR? $($Round your answer to two decimal places$)$

Interpret the interquartile range $($Select all that apply.$).$

Measures the location of a quantitative variable

A measure of dissimilarity

The difference between the largest and smallest values

Measures the spread of the middle $50\%$ of the sorted data

A measure of similarity

A measure of dispersion

The difference between the $1$st and $2$nd quartiles

The total distance the values of a quantitative variable span from end to end $($i$.$e$.,$ from smallest to largest$)$

A measure of central tendency

$($e$).$ What is the probability that the USD$/$CHF closing rate for any given day is between $0\mathrm{.}65$ and $0\mathrm{.}95?($Round your answer to four decimal places$)$

What is the $20$ th percentile? $($Round your answer to the nearest cent$)$

What percent of closing rates fall between $0\mathrm{.}73$ and $0\mathrm{.}85?($Round your answer to two decimal places$)$

$($e$)$ What is the probability that the USD$/$CHF closing rate for any given day is between $0\mathrm{.}65$ and $0\mathrm{.}95?($Round your ans$)$ to four decimal places$)$

What is the $20$th percentile? $($Round your answer to the nearest cent$)$

What percent of closing rates fall between $0\mathrm{.}73$ and $0\mathrm{.}85?($Round your answer to two decimal places$)$

$\%$

What is