Question 1083275: 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 percent confidence in the radius of the donuts are within 0.25cm, rather than measure each and every donut that is baked?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Use a stats table to find that the critical value is roughly z = 1.645
To find this value, locate "90%" at the bottom (in the Confidence Level section) and the value just above this entry is 1.645
The population standard deviation sigma is given to be sigma = 1.25
The margin of error desired is 0.25, so E = 0.25
------------------------------------------------------------------------------------------------------------------------
We will plug z = 1.645, sigma = 1.25 and E = 0.25 into the formula below to find n.
n = ( (z*sigma)/E )^2
n = ( (1.645*1.25)/0.25 )^2
n = ( 2.05625/0.25 )^2
n = ( 8.225 )^2
n = 67.650625
n = 68 ... round up to the nearest whole number
Min Sample Size: n = 68
So this means that she can use a sample size of 68 or larger.
She should take at least 68 measurements to ensure that the radius of the donuts is within +- 0.25cm.
|
|
|
