The seventh-grade class is building target areas for a PE activity. The bases for the game will be circular in shape. The diamet
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Answer:
And we can use the z score formula given by:
And using the z score we have:
And we can use the normal standard distribution table or excel in order to find the probabilities and we got:
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".
Solution to the problem
Let X the random variable that represent the time it takes her to complete one review, and for this case we know the distribution for X is given by:
Where and
And we select a sample size of n =16. Since the dsitribution for X is normal then the distribution for the sample mean is also normal and given by:
For this case we want to find this probability:
And we can use the z score formula given by:
And using the z score we have:
And we can use the normal standard distribution table or excel in order to find the probabilities and we got:
The graph illustrating the problem is on the figure attached.
