the state test scores for 12 randomly selected high school seniors are shown on the right. complete parts…

Explanation:

Step1: Recall the formula for sample standard deviation

The formula for the sample standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}), where (n) is the sample size, (x_{i}) are the data points, and (\bar{x}) is the sample mean. Here (n = 12) and (\bar{x}=911.0).

Step2: Calculate ((x_{i}-\bar{x})^{2}) for each data point

For (x_1 = 1427): ((1427 - 911)^{2}=(516)^{2}=266256) For (x_2 = 1228): ((1228 - 911)^{2}=(317)^{2}=100489) For (x_3 = 987): ((987 - 911)^{2}=(76)^{2}=5776) For (x_4 = 699): ((699 - 911)^{2}=(- 212)^{2}=44944) For (x_5 = 725): ((725 - 911)^{2}=(-186)^{2}=34596) For (x_6 = 830): ((830 - 911)^{2}=(-81)^{2}=6561) For (x_7 = 726): ((726 - 911)^{2}=(-185)^{2}=34225) For (x_8 = 748): ((748 - 911)^{2}=(-163)^{2}=26569) For (x_9 = 544): ((544 - 911)^{2}=(-367)^{2}=134689) For (x_{10}=627): ((627 - 911)^{2}=(-284)^{2}=80656) For (x_{11}=1441): ((1441 - 911)^{2}=(530)^{2}=280900) For (x_{12}=950): ((950 - 911)^{2}=(39)^{2}=1521)

Step3: Sum up ((x_{i}-\bar{x})^{2})

(\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}=266256+100489 + 5776+44944+34596+6561+34225+26569+134689+80656+280900+1521) (\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}=1022181)

Step4: Calculate the sample standard deviation

(s=\sqrt{\frac{1022181}{12 - 1}}=\sqrt{\frac{1022181}{11}}\approx\sqrt{92925.545}\approx304.8)

Answer:

(s = 304.8)