Question

# the San Andres Mountains gave the following weights (pounds): 68 106 133 130 60 64 Assume...

the San Andres Mountains gave the following weights (pounds):

 68 106 133 130 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 68,106,133,130,60,64

(a) Mean x = 93.5

Explanation :-

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:

=> Mean = Sum of terms/Number of terms

Sum of terms = 68 + 106 + 133 + 130 + 60 + 64 = 561

Number of terms = 6

mean = Sum of terms/Number of terms = 561/6 = 93.5

(b) standard deviation s = 33.7

(b) n = 6 , df = n-1 = 5

=> For 75% confidence interval , t = 0.130

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

= 93.5 +/- 0.130*33.7/sqrt(6)

= (91.7,95.3)

=> Lower limit = 91.7

=> Upper limit = 95.3