Question

From past experience it is known that the weights of salmon grown at a commercial hatchery are normal with a mean that varies from season to season but with a standard deviation that remains fixed at 0.3 pounds. If we want to be 95 percent certain that our interval estimate of the present season’s mean weight of a salmon is of width 0.2, then the suitable sample size needed is:

		10
		127
		None
		35
		87

Answer 1

Solution

standard deviation =   =0.3

Margin of error = E = width/2=0.2/2=0.1

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96*0.3 /0.1 )2

n =35

Sample size = n =35