Respuesta :
Answer:
Correct option: B. 90%
Explanation:
The confidence interval is given by:
[tex]CI = [\bar{x} - z\sigma_{\bar{x}} , \bar{x}+z\sigma_{\bar{x}} ][/tex]
If [tex]\bar{x}[/tex] is 190, we can find the value of [tex]z\sigma_{\bar{x}}[/tex]:
[tex]\bar{x} - z\sigma_{\bar{x}} = 188.29[/tex]
[tex]190 - z\sigma_{\bar{x}} = 188.29[/tex]
[tex]z\sigma_{\bar{x}} = 1.71[/tex]
Now we need to find the value of [tex]\sigma_{\bar{x}}[/tex]:
[tex]\sigma_{\bar{x}} = s / \sqrt{n}[/tex]
[tex]\sigma_{\bar{x}} = 5/ \sqrt{25}[/tex]
[tex]\sigma_{\bar{x}} = 1[/tex]
So the value of z is 1.71.
Looking at the z-table, the z value that gives a z-score of 1.71 is 0.0436
This value will occur in both sides of the normal curve, so the confidence level is:
[tex]CI = 1 - 2*0.0436 = 0.9128 = 91.28\%[/tex]
The nearest CI in the options is 90%, so the correct option is B.
