Question $2[10]$

Statistical analysis of past data for automatic teller machine $($ATM$)$ withdrawals at a certain bank shows that the amounts withdrawn per day range between R$800$ and R$2000$ per customer with the following frequencies:

Amount per withdrawal R$800$ R$900$ R$1000$ R$1500$ R$2000$

Frequency $($number of customers per day$)$

$9$

$20$

$18$

$10$

$3$

$2\mathrm{.}1$ Convert the frequency table to a cumulative probability distribution. $(3)$

$2\mathrm{.}2$ Suppose the initial amount of cash available at the ATM on a certain day is R$60000.$ Can the bank expect a shortfall of cash at the ATM on that day? $(3)$

$2\mathrm{.}3$ Simulate cash withdrawal at the ATM for the rst $10$ customers of the day and nd the remaining amount of cash at the ATM given that the initial amount for the day is R$30000.$ Use the following U$[0,1)-$random numbers:

U$1=0\mathrm{.}53$; U$2=0\mathrm{.}73$; U$3=0\mathrm{.}76$; U$4=0\mathrm{.}82$; U$5=0\mathrm{.}61$; U$6=0\mathrm{.}20$; U$7=0\mathrm{.}75$; U$8=0\mathrm{.}75$; U$9=0\mathrm{.}12$; U$10=0\mathrm{.}14$