Answer:
a)
b)
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".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
(a) What are the mean and standard deviation of the sampling distribution?
On this case
(b) What is the approximate probability that x will be within 0.4 of the population mean μ? (Round your answer to four decimal places.) P =
So for this case we want this probability:
And for this case we can use the z score given by this formula:
And using this concept we got this:
