Respuesta :
Answer:
a. $134.66
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".
[tex]\bar X =128[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=38 represent the sample standard deviation
n=100 represent the sample size
2) Calculate the confidence interval
Since the sample size is large enough n>30. The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]128-1.64\frac{38}{\sqrt{100}}=121.768[/tex]
[tex]128+1.64\frac{38}{\sqrt{100}}=134.232[/tex]
The closest value would be $134.66 and that would be the answer for this case.
