QUESTION $2(29$ marks$)$ Snack & Crack Ltd $($Snack & Crack$)$ is a candy and chips manufacturer located in Johannesburg CBD$.$ The entity has a $31$ July financial yearend. Snack & Crack$$s product development department continuously evaluates the current products' success and develops ideas for new products. If it is deemed that the new product has a high enough potential success rate, it is manufactured and added to the current product range that Snack & Crack offers. The product development department is evaluating two possible new products $$ Rizz and Sigma. Only one of the two will be selected to be introduced to the market. Both Rizz and Sigma are chips, but while Rizz has a more traditional taste, Sigma is more exotic. Consequently, it is certain that Rizz will be accepted by the market and sold but Sigma's success is more uncertain. Should Sigma however be popular in the market, the returns generated from the quantity sold will greatly out perform Rizz$$s returns which will be more conservative. In order to evaluate which product to choose, Snack & Crack has conducted research on the probability of each product$$s success and the returns they will receive in each of the various outcomes. RIZZ: Potential outcomes Probability Return if this outcome manifests Highly popular $29\%31\%$ Average $?25\%$ Fails $13\%19\%7$ HFMN$230-1\_$Jan$-$Jun$2025\_$FA$2\_$V$3\_$ES$\_27012025$ SIGMA: Potential outcomes Probability Return if this outcome manifests Highly popular $26\%42\%$ Average $38\%29\%$ Fails $?14\%$ REQUIRED: $2\mathrm{.}1$ Calculate the expected returns of Rizz and Sigma, respectively. $(8$ marks$)2\mathrm{.}2.$ Calculate the risk attached to investing in Sigma. $(14$ marks$)$ Communication skill: Presentation $(1$ mark$)2\mathrm{.}3.$ Calculate the chance of Sigma$$s return to be $35\%$ or less. Assume an expected return of $22\%,$ a risk of $9\mathrm{.}8\%,$ and a normal distribution.