A department store is running a promo one Saturday by giving out coupons for $10 of free merchandise. However, one-third of customers spend $40, and one-third spend$75. The remainder of customers who come in the store do not take advantage of the promo at all.
A) find expected value for the dept store on their promo.
B) if the store has 712 customers on the promo Saturday, what is their net expected profit at the end of the day?
To find the expected value for the department store on their promo, we need to calculate the probability of each scenario and then multiply it by the corresponding outcome value.
Given information:
- One-third of customers spend $40.
- One-third of customers spend $75.
- The remaining customers do not take advantage of the promo.
Let's start with calculating the probabilities:
The probability of a customer spending $40 is 1/3 or 33.33% (since one-third is equal to 33.33%).
The probability of a customer spending $75 is also 1/3 or 33.33%.
To find the probability of a customer not taking advantage of the promo, we need to subtract the probabilities of the other two scenarios from 100%:
Probability of not taking advantage of the promo = 100% - (33.33% + 33.33%) = 33.33%.
Now, we can calculate the expected value for the department store:
Expected value = (Probability of spending $40 * Value of spending $40) + (Probability of spending $75 * Value of spending $75) + (Probability of not taking advantage of promo * Value of not taking advantage)
Expected value = (33.33% * $40) + (33.33% * $75) + (33.33% * $0)
Expected value = $13.33 + $25 + $0
Expected value = $38.33
Therefore, the expected value for the department store on their promo is $38.33.
To calculate the net expected profit at the end of the day, we need to multiply the expected value by the number of customers:
Net expected profit = Expected value * Number of customers
Given that there are 712 customers on the promotional Saturday:
Net expected profit = $38.33 * 712
Net expected profit = $27,289.96
Therefore, the department store's net expected profit at the end of the day is approximately $27,289.96.