How much do wild mountain lions weigh?

Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (in pounds):

69, 103, 126, 122, 60, 64

Assume that the population of \( x \) values has an approximately normal distribution.

Use a calculator with mean and sample standard deviation keys to find the sample mean weight \(\bar{x}\) and sample standard deviation \(s\). (Round your answers to one decimal place.)

\(\bar{x} = \) lb

\(s = \) lb

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.