Question

# How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured...

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 (pounds): 66 106 133 130 60 64

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

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

x = ?? lb

s = ?? lb

(b) Find a 75% confidence interval for the population average weight ? of all adult mountain lions in the specified region. (Round your answers to one decimal place.) lower limit = ?? lb

upper limit = ?? lb

solution :

Given that 66 , 106 , 133 , 130 , 60 , 64

(a) Sum of terms = 66 + 106 + 133 + 130 + 60 + 64 = 559

Number of terms = 6

=> Mean x = Sum of terms/Number of terms

= 559/6

= 93.2 (rounded)

=> The standard deviation of the data set is s = 34.0 (rounded)

(b) n = 6

=> df = n - 1 = 5

=> for 75% confidence interval , t = 1.3

=> The 75% confidence interval for the population mean is x +/- t*s/sqrt(n)

=> 93.2 +/- 1.3*34.0/sqrt(6)

=> (75.2 , 111.3)

=> Lower limit = 75.2

=> Upper limit = 111.3

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