Tatooine is a fictional desert planet that appears in the Star Wars franchise. It is home to many settlers, including humans. Let X = weight of a human inhabitant on Tatooine. You know from prior research that X is approximately Normally distributed with population mean u = 96kg and population standard deviation o = 23.3kg. A. Specify the sampling distribution of statistic X, including stating what (5pts) type of distribution, its sampling mean uy, and its standard deviation Oy, for samples of 9 humans living on Tatooine. B. What is the Probability that a randomly selected group of 9 humans on (10pts) Tatooine would have a mean weight between 95 and 100kg? Include a rough sketch and Probability statement.

a) For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

With the following parameters:

b)

And we can use the z score formula given by:

And if we find the z score for the limit we got:

The sketch is on the figure attached

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 weights of a population, and for this case we know the distribution for X is given by:

Where and

Part a

For this case we select a sample size of n =9. And the distribution for the sample mean is given by:

With the following parameters:

Part b

For this case we want this probability:

And we can use the z score formula given by:

And if we find the z score for the limit we got:

The sketch is on the figure attached

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1