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C) (-5%.15%)
Step-by-step explanation:
1) Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
represent the sample mean for the sample
population mean (variable of interest)
=5% =0.05 represent the population standard deviation
2) Confidence interval
We assume that the random variable X who represent The Ishares Bond Index fund (TLT) follows this distribution:
The confidence interval for the returns on TLT is given by the following formula:
(1)
In order to calculate the critical value . Since the Confidence is 0.66 or 66%, the value of
and
, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.17,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 66% confidence interval would be given by (-0.05;0.15) and we can convert this into % and wr got (-5%; 15%).