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Answer :
The sample mean weight of the wild mountain lions is 90.7 pounds, and the sample standard deviation is 30.0 pounds. These values were calculated using the given data set of weights.
To find the sample mean weight (x) and the sample standard deviation (s) of the wild mountain lions, we first list the weights: 69, 103, 126, 122, 60, 64 pounds.
Step-by-step Calculation:
Calculate the sample mean weight:
x = (69 + 103 + 126 + 122 + 60 + 64) / 6 = 544 / 6 = 90.7 lb
Calculate the deviations from the mean and square them:
(69 - 90.7)² = 475.69
(103 - 90.7)² = 151.29
(126 - 90.7)² = 1254.49
(122 - 90.7)² = 975.69
(60 - 90.7)² = 950.49
(64 - 90.7)² = 707.29
Total = 4514.94
Divide by the number of data points minus 1 (n - 1): s² = 4514.94 / 5 = 902.988
Take the square root to find the sample standard deviation: s = √902.988 ≈ 30.0 lb
Thus, the sample mean weight is 90.7 pounds and the sample standard deviation is 30.0 pounds.
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