Question

The Ishares Bond Index fund (TLT) has a mean and annual standard deviation of returns of 5%

Answer 1

Answer:

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".

$\bar X =10\%=0.1$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)

$\sigma$=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:

$X \sim N(\mu, \sigma=10\%=0.1)$

The confidence interval for the returns on TLT is given by the following formula:

$\bar X \pm z_{\alpha/2}\sigma$   (1)

In order to calculate the critical value $z_{\alpha/2}$. Since the Confidence is 0.66 or 66%, the value of $\alpha=0.34$ and $\alpha/2 =0.17$, 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 $z_{\alpha/2}=0.95$

Now we have everything in order to replace into formula (1):

$0.05-0.95(0.1)=-0.05$    

$0.05+0.95(0.1)=0.15$

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%).