Question

Owners of an exercise gym believe that a Normal model is useful in projecting the number of clients who will exercise in their gym each

week. They use a mean of 800 clients and a standard deviation of 90 clients.
During the holidays the lowest 10% of clients visit the gym. What is the maximum number of clients that visit the gym?
980
915
620
685

Answer 1

To find the maximum number of clients that visit the gym during the holidays, we need to calculate the cutoff value for the lowest 10% of clients. By using the z-score formula and solving for X, we find that the maximum number of clients is approximately 685.

Step-by-step explanation:

To find the maximum number of clients that visit the gym during the holidays, we need to find the cutoff value for the lowest 10% of clients. In a Normal distribution, the cutoff value for a particular percentile can be found by using the z-score formula. The z-score is calculated by subtracting the mean from the desired value and dividing by the standard deviation. The cutoff value for the lowest 10% of clients corresponds to a z-score of -1.28. So, to find the maximum number of clients, we can use the formula: z-score = (X - mean) / standard deviation, and solve for X.

z-score = (X - 800) / 90

-1.28 = (X - 800) / 90

-1.28 * 90 = X - 800

-115.2 = X - 800

X = 800 - 115.2

X = 684.8

Therefore, the maximum number of clients that visit the gym during the holidays is approximately 685.