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 98% confidence to within 0.1 lb, the average force required to break the binding? Assume that σ is known to be 0.6 lb. (Use the value of z rounded to two decimal places.)

Answer 1

Answer: 196

Step-by-step explanation:

As per given , we have

Population standard deviation: $\sigma=0.6\ lb$

Significance level : $\alpha: 1-0.98=0.02$

Using the z-value table , the critical z value for 98% confidence : $z_{\alpha/2}=2.33$

Margin of error : E= 01 lb

Sample size : $n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2$

$n=(\dfrac{(2.33)\cdot(0.6)}{0.1})^2$

Simplify , we get

$n=195.4404\approx196$

Hence, the minimum sample size required for books = 196