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Jovan Perovic · Answer 1 · 2021-03-24T13:59:24+0000

Answer:

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_(\alpha/2)(\sigma)/(√(n))$ (1)

Since the Confidence is 0.95 or 95%, the value of
$\alpha=0.05$ and
$\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
$z_(\alpha/2)=1.96$

The standard error for this case is given:

$SE =(\sigma)/(√(n))=1$

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

2-1.96*11=0.04

2+1.96*1=3.96

Step-by-step explanation:

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".

$\bar X =2$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Calculate the confidence interval