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Complete Question:
The mean weight of salmon at a fishery is 15.8 pounds, with a standard deviation of 2.4 pounds. A researcher records the weight of the following salmon. 14.5lbs, 16.8lbs, 15lbs, 16.4lbs, and 15.9 lbs. Find µ,σ, x, and s
Answer
μ = 15.8 pounds
σ = 2.4 pounds
Mean = 15.72 pounds
s = 0.958 pounds
Step by Step explanation:
a) μ is the population mean and it is given in the question already as 15.8 pounds.
b) Sample Mean : The formula is given as Summation of the number of term/ Total number of terms
Sample Mean= (14.5 + 16.8 +15 + 16.4 + 15.9) / 5
Sample Mean= 15.72 pounds
c) σ is the population standard
deviation
This has already be given to us in the question as the standard deviation of the fish which is 2.4 lbs
d) s is the sample standard deviation
The formula for standard deviation is
s = √∑(x- Sample mean)² / (n-1))
Where :
Sample mean = 15.72 lbs
n = total number of terms = 5
Therefore, s =
√([(14.5- 15.72)²+ (16.8 -15.72)²+ (15 - 15.72)² + (16.4 - 15.72)² + (15.9 - 15.72)² ]/ 5 - 1)
s = √(3.67/4)
s = √0.9175
s = 0.957862203 lbs
s = 0.958 lbs