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 and s.

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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