The Stop N’ Go convenience chain recently selected a random sample of 10 customers. The store monitored the number of times each customer made a purchase at the store over a two-month period. The following data were collected:

10 19 17 19 12 20 20 15 16 13

a. Store executives are considering a promotion in which they reward frequent purchases with a small gift. They have decided that they will only give gifts to those shoppers whose number of visits in the previous two-month period is above the mean plus one standard deviation. Find the minimum number of visits required to receive a price.

Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

I'll let you do the calculations.

20

To find the minimum number of visits required to receive a gift, we need to calculate the mean and standard deviation of the given data.

Step 1: Calculate the mean (average) of the data.
To calculate the mean, add up all the numbers and divide by the total number of data points:

10 + 19 + 17 + 19 + 12 + 20 + 20 + 15 + 16 + 13 = 161

Mean = 161 / 10 = 16.1

Step 2: Calculate the standard deviation of the data.
To calculate the standard deviation, we first need to find the variance. The variance is the average of the squared differences between each data point and the mean. Here's how you can calculate it:

1. Subtract the mean from each data point:
10 - 16.1 = -6.1
19 - 16.1 = 2.9
17 - 16.1 = 0.9
19 - 16.1 = 2.9
12 - 16.1 = -4.1
20 - 16.1 = 3.9
20 - 16.1 = 3.9
15 - 16.1 = -1.1
16 - 16.1 = -0.1
13 - 16.1 = -3.1

2. Square each of these differences:
(-6.1)^2 = 37.21
(2.9)^2 = 8.41
(0.9)^2 = 0.81
(2.9)^2 = 8.41
(-4.1)^2 = 16.81
(3.9)^2 = 15.21
(3.9)^2 = 15.21
(-1.1)^2 = 1.21
(-0.1)^2 = 0.01
(-3.1)^2 = 9.61

3. Calculate the variance by finding the average of these squared differences:
(37.21 + 8.41 + 0.81 + 8.41 + 16.81 + 15.21 + 15.21 + 1.21 + 0.01 + 9.61) / 10 = 10.4

4. Calculate the standard deviation by taking the square root of the variance:
√10.4 = 3.23

Step 3: Calculate the minimum number of visits required to receive a gift.
The minimum number of visits required to receive a gift is the mean plus one standard deviation:

Minimum number of visits = Mean + 1 * Standard deviation
Minimum number of visits = 16.1 + 1 * 3.23
Minimum number of visits = 16.1 + 3.23
Minimum number of visits ≈ 19.33

Therefore, the minimum number of visits required to receive a gift is approximately 19.33 visits.