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:


Answer:
38.28 years
Step-by-step explanation:
The computation of the time period is shown below:
Given that
RATE = 6.2%
PV = $500
PMT = $0
FV = $5,000
The formula is shown below:
= NPER(RATE;PMT;-PV;FV;TYPE)
After applying the above formula, the time period is 38.28 years
Hence, in order to save $5,000 it would take 38.28 years
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One. that is the definition of a line.
Through any two points, there is exactly one line.