Answer:
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
