Respuesta :
Answer:
[tex] z = \frac{205-233.3396}{37.498}= -0.76[/tex]
So then the value of 205 it's 0.76 deviations below the population mean on this case
Step-by-step explanation:
For this case we have the following data given:
177, 205, 210, 210, 232, 205, 185, 185, 178, 210, 206, 212, 184, 174, 185, 242, 188, 212, 215, 247, 241, 223, 220, 260, 245, 259, 278, 270, 280, 295, 275, 285, 290, 272, 273, 280, 285, 286, 200, 215, 185, 230, 250, 241, 190, 260, 250, 302, 265, 290, 276, 228, 265
And these values represent the weigths of all the team members of the Arizona Cardinals
Now if we organize the data values from the smallest to the largest we have:
174 177 178 184 185 185 185 185 188 190 200 205 205 206 210 210 210 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302
For this case we can calculate the mean with the following formula:
[tex] \mu = \frac{\sum_{i=1}^n X_i}{n}[/tex]
And if we replace we got:
[tex] \mu = 233.3396[/tex]
And for the deviation we can use the following formula:
[tex] \sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And if we replace we got:
[tex] \sigma = 37.498[/tex]
And in order to calculate How many standard deviations above or below the mean was he we can use the z score formula given by:
[tex] z = \frac{x -\mu}{\sigma}[/tex]
And we assume that x=205 and if we replace we have:
[tex] z = \frac{205-233.3396}{37.498}= -0.76[/tex]
So then the value of 205 it's 0.76 deviations below the population mean on this case
