Janet Is Planning to Rent a Booth at a Festival $\$ 80$

Multiple Choice

Janet is planning to rent a booth at a festival for a day to sell clothes that she has made.She sells jackets for $\$ 80$ and skirts for $\$ 50$ Her past experiences suggests that sales of jackets will have a mean of 6.5 with a standard deviation of $\sigma _ { j }$ ,and sales of skirts will have a mean of 12.6 with a standard deviation of $\sigma _ { s }$ .The cost of renting the booth for the day is $\$ 180$ Let the random variable J represent the number of jackets that Janet sells and the random variable S represent the number of skirts that Janet sells.Then Janet's net income,I,is given by the expression: I = 80J + 50S - 180
Find an expression for the standard deviation of Janet's net income.Assume that sales are independent of each other.

A) ? = 80 $\sigma _ { j }$ + 50 $\sigma _ { s }$
B) ? = $\sqrt { 6400 \sigma _ { j } ^ { 2 } + 2500 \sigma _ { s } ^ { 2 } - 180 }$
C) ? = $\sqrt { 80 \sigma _ { j } ^ { 2 } + 50 \sigma _ { s } ^ { 2 } }$
D) ? = $\sqrt { 6400 \sigma _ { j } ^ { 2 } + 2500 \sigma _ { s } ^ { 2 } }$
E) ? = 80 $\sigma _ { j }$ + 50 $\sigma _ { s }$ - 180