Question

Mona wants to obtain a 94% confidence interval for the mean weight of turtles. She read in the Big Book of Turtles that the standard deviation of turtle weight is 37 grams. If her confidence interval must have a length of no more than 15, how many turtles must she weigh?

Answer 1

87

Explanation:

Population standard deviation = σ = 37 grams

Confidence interval = 94%

(1-α)×100% = 94

⇒α = 0.06

From table z table and interpolation

z = 1.881

L = Confidence interval length = 15

N = Number of samples

`L=2z_(\alpha/2)(\sigma)/(\sqrt N)\\\Rightarrow \sqrt N=2z_(\alpha/2)(\sigma)/(L)\\\Rightarrow \sqrt N=2* 1.881(37)/(15)\\\Rightarrow \sqrt N=9.2796\\\Rightarrow N=86.11097616\approx 87`

∴ Number of turtles must she must weigh is 87