Anutrition laboratory wants to construct a 95% confidence interval for the mean sodium content of "reduced sodium" hot dogs. a preliminary study of reduced sodium hot dogs gives a standard deviation of 25mg of sodium. how many hot dogs should the researchers sample in order for the width of their confidence interval to be no more than 10 mg?

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg

Step-by-step explanation:

Given;

Standard deviation r= 25mg

Width of confidence interval w= 10mg

Confidence interval of 95%

Margin of error E = w/2 = 10mg/2 = 5mg

Z at 95% = 1.96

Margin of error E = Z(r/√n)

n = (Z×r/E)^2

n = (1.96 × 25/5)^2

n = (9.8)^2

n = 96.04

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2