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<u>Question</u>
Suppose that a committee is studying whether or not there is excessive time waste in our judicial system. It is interested in the mean amount of time individuals spend at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was 4 hours with a sample standard deviation of 1.2 hours. Define the random variables X and in words.
Answer:
(B)
- X is the amount of time an individual waits at the courthouse to be called for service.
is the mean wait time for a sample of individuals.
Step-by-step explanation:
The random variable X is the amount of time for which each of the prospective juror waits at the courthouse before being called for service.
is the mean wait time for a the given sample of individuals. In the case given,
Answer:
And using a calculator, excel or the normal standard table we have that:
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 weigths of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
We can find the probability required with the following z score formula:
And replacing we got:
And using a calculator, excel or the normal standard table we have that: