## A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator. Is it appro

Question

A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator. Is it appropriate to use the normal distribution to find probabilities for x?

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2021-11-17T14:28:05+00:00
2021-11-17T14:28:05+00:00 1 Answer
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## Answers ( )

Answer:Where and

Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

So then is appropiate use the normal distribution to find the probabilities for

Step-by-step explanation:Previous conceptsNormal 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-scoreis “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”. The letter is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:Solution to the problemLet X the random variable that represent the variable of interest 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 the distribution for the sample mean is also normal and given by:

So then is appropiate use the normal distribution to find the probabilities for