Questions: 179 ; 202 ; 212 ; 212 ; 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 Assume the population was Football Team A. Find the following. (Round your answers to two decimal places) (i) the population mean, μ 227.42 (ii) the population standard deviation, σ (iii) the weight that is 3 standard deviations below the mean 94.49 (iv) When Player A played football he weighed 225

Solution Steps

To solve the given problem, we need to:

1. Sort the data from smallest to largest value.
2. Calculate the population mean.
3. Calculate the population standard deviation.
4. Find the weight that is 3 standard deviations below the mean.

The given data is sorted from smallest to largest value: \[ [174, 178, 179, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 212, 212, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302] \]

The population mean, \(\mu\), is calculated as: \[ \mu = 236.3962 \]

The population standard deviation, \(\sigma\), is calculated as: \[ \sigma = 37.4379 \]

The weight that is 3 standard deviations below the mean is calculated as: \[ \mu - 3\sigma = 236.3962 - 3 \times 37.4379 = 124.0825 \]

Final Answer