Question

A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested to estimate with 99% confidence to within 0.1 lb, the average force required to break the binding? Assume that σ is known to be 0.7 lb. (Use the value of z rounded to two decimal places.)

Answer 1

Solution :

Given that,

standard deviation =   =0.7

Margin of error = E = 0.1

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58 ( Using z table ( see the 0.005 value in standard normal (z) table corresponding z value is 2.58 )  

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

n = ( 2.58* 0.7 / 0.1 )2

n =326.16

Sample size = n =327