Respuesta :
Answer
• a) $90.50
,• b) $29.29
,• c) $73.63
,• d) $107.37
Explanation
Given the data, we can calculate the mean and standard deviation using a software.
• a)
That software will use the following formula for the mean:
[tex]\bar{x}=\frac{sum\text{ of all observations}}{total\text{ number of observations}}[/tex]In our case, we have 20 observations, meaning:
[tex]\bar{x}=\frac{95+120+40+...+90+70+100}{20}=90.5[/tex]• b)
Similarly, for the standard deviation s the formula is:
[tex]s=\sqrt{\frac{\sum_^(x-\bar{x})}{n-1}}[/tex]where x represents each observation.
Then, using the software we would get:
[tex]s\approx29.29[/tex]Finally, the confidence interval (CI) can be calculated using the following formula:
[tex]CI=\bar{x}\pm Z\times\frac{s}{\sqrt{n}}[/tex]Replacing the data we get:
[tex]CI=90.5\pm2.5758\times\frac{29.29}{\sqrt{20}}\approx90.5\pm16.87[/tex]Meaning that the upper limit will be:
[tex]90.5+16.87=107.37[/tex]While the lower will be:
[tex]90.5-16.87=73.63[/tex]