Question 1083253: A donut baker wants to ensure that the radius of its donuts is within +- 0.25cm. Based on past statistical studies, she knows that the donut’s radius has a standard deviation of 1.25cm. How many measurements should she take to ensure a 90% confidence in the radius of the donuts are within 0.25cm, rather than measure each and every donut that is baked?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The interval is +/-0.25 cm
90%CI start with z and see if large enough not to use t
1.645*1.25/sqrt(n)<=0.25
multiply by sqrt(n)
2.05625 <=0.25n
square both sides
4.23<0.0625 n
divide by 0.0625
67.65 which rounds up to 68.
t for df=67, n=68, is 1.67
1.67*1.25/sqrt(68)=0.253, which is just a little high.
1.668*1.25/sqrt(69)=0.251
use 70
1.667*1.25/sqrt(70)=0.2491
n=70
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