A Gym Knows That Each Member, on Average, Spends 70

question 2

Short Answer

A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed.
A) What is the probability that a randomly selected customer spends less than 65 minutes at the gym?
B) Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
C) If 49 members are randomly selected, what is the probability that the average time spent at the gym exceeds 75 minutes?

• A) What is the probability that a randomly selected customer spends less than 65 minutes at the gym?
• B) Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
• C) If 49 members are randomly selected, what is the probability that the average time spent at the gym exceeds 75 minutes?

---

Definitions:

Shortage Costs

The costs incurred when demand exceeds supply, including lost sales, expedited shipping fees, and decreased customer satisfaction.

Disrupted Production

Interruptions in the normal flow of manufacturing processes due to unforeseen events, leading to delays and potential financial losses.

Lost Sales

The potential revenue that a company misses out on due to being out of stock, having insufficient capacity, or other reasons for not fulfilling customer demand.

Quantity Discounts

Price reductions applied to bulk purchases, incentivizing buyers to increase the volume of their purchase.