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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?

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Definitions:

Hundreds of Studies

A phrase indicating a large body of research work or experiments focusing on a particular topic or field.

Meta-Analysis

A statistical technique for combining the results of multiple studies to arrive at a comprehensive conclusion.

Experiments

Controlled procedures carried out to discover, demonstrate, or test a hypothesis, involving manipulation of variables to observe effects.

Combining

The action or process of merging two or more elements together.