Question

Belk Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their Belk credit card will be given a special Belk Lottery card. The customer will scratch off the card, which will indicate the amount to be taken off the total amount of the purchase. Listed below are the amount of the prize and the percent of the time that amount will be deducted from the total amount of the purchase. Prize Amount Probability $ 10 .50 25 .40 50 .08 100 .02 (a) What is the mean amount deducted from the total purchase amount? (b) What is the standard deviation of the amount deducted from the total purchase?

Answer 1

The mean amount deducted from the total purchase amount is $21, and the standard deviation is $25.49.

Step-by-step explanation:

To find the mean amount deducted from the total purchase amount, we need to multiply each prize amount by its corresponding probability and then sum up the results. The calculation would look like this:

(10 * 0.50) + (25 * 0.40) + (50 * 0.08) + (100 * 0.02) = 5 + 10 + 4 + 2 = 21

The mean amount deducted from the total purchase amount is $21.

To find the standard deviation of the amount deducted from the total purchase, we can use the formula:

√[((10 - 21)^2 * 0.50) + ((25 - 21)^2 * 0.40) + ((50 - 21)^2 * 0.08) + ((100 - 21)^2 * 0.02)]

This calculation would give us the standard deviation, which is approximately $25.49. The standard deviation of the amount deducted from the total purchase is $25.49.

Answer 2

The mean amount deducted from the total purchase amount is $21. The standard deviation of the amount deducted from the total purchase amount is $38.25.

Step-by-step explanation:

To find the mean amount deducted from the total purchase amount, we multiply each prize amount by its corresponding probability and sum them up:

1. Multiply $10 by 0.50: $10 * 0.50 = $5
2. Multiply $25 by 0.40: $25 * 0.40 = $10
3. Multiply $50 by 0.08: $50 * 0.08 = $4
4. Multiply $100 by 0.02: $100 * 0.02 = $2

Add these amounts together: $5 + $10 + $4 + $2 = $21

Therefore, the mean amount deducted from the total purchase amount is $21.

To find the standard deviation of the amount deducted from the total purchase, we use the formula:

Standard deviation = square root of [(prize amount - mean) squared multiplied by its probability]

1. For $10, the calculation is: (10 - 21)^2 * 0.50 = 55
2. For $25, the calculation is: (25 - 21)^2 * 0.40 = 6.4
3. For $50, the calculation is: (50 - 21)^2 * 0.08 = 87.36
4. For $100, the calculation is: (100 - 21)^2 * 0.02 = 1314.96

Add these amounts together: 55 + 6.4 + 87.36 + 1314.96 = 1463.72

Take the square root of the sum: square root of 1463.72 = 38.25

Therefore, the standard deviation of the amount deducted from the total purchase amount is $38.25.