A fitness center is interested in the average amount of time a client exercises in the center each week. Match the vocabulary wo
rd with its corresponding example.
1 answer:
Answer:
Step-by-step explanation:
A. Data of the study: All 45 exercise times there were recorded from the participants in the study
B. Parameter of the study: The average amount of time that all clients exercise in one week.
C. Variable of the study: The amount of time that any given client from the fitness center exercises.
D. Population for the study: All clients at the fitness center.
E. Sample of this study: The 45 client from the fitness center who participated in the study.
F. Statistics of the study: The average amount of time that a sample of clients exercises in one week
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Answer:
The probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is 0.9973.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
Solution to the problem
We are interested on this probability
If we apply the Z score formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
The probability that Albert's sample of 64 will have a mean between 13.5 and 16.5 minutes is 0.9973.