Gold’s Gym selected a random sample of 10 customersand monitored the number of times each customer usedthe workout facility in a one-month period. Thefollowing data were collected:10 19 17 19 12 20 20 15 16 13Gold’s managers are considering a promotion in whichthey reward frequent users with a small gift. They havedecided that they will only give gifts to those customerswhose number of visits in a one-month period is 1standard deviation above the mean. Find the minimumnumber of visits required to receive a gift

Kindly check explanation

Step-by-step explanation:

Number of times 10 randomly selected sample of customers used workout facility in 1 month :

10 19 17 19 12 20 20 15 16 13

Users to be rewarded are those whose visit is one standard deviation above the mean.

Hence, we need to calculate the mean and standard deviation of the sample:

To save computation time, we can obtain the mean and standard deviation of the sample using excel or calculator :

Mean: Σ(X) / n

n = number of observations

Mean = (10 + 19 + 17 + 19 + 12 + 20+ 20+ 15+ 16 + 13) / 10

= 161 / 10

= 16.1

Standard deviation (s) of a sample:

Sqrt[Σ(X - m)²/(n - 1)]

Using a calculator, this gives 3.542 = 3.5

Hence,

1 standard deviation above the mean :

(16. 1 + 3.5) = 19.6