Answer: 1534
Step-by-step explanation:
The formula used to find the sample size :-
[tex]n=(\dfrac{z_{\alpha/2}\cdot\sigma}{E})^2[/tex] , where [tex]\sigma=[/tex] Population standard deviation.
E= Margin of error
[tex]z_{\alpha/2}[/tex]= Two-tailed z-value for significance level of [tex]\alpha[/tex].
Given : Confidence level : 99%
Then significance level : [tex]\alpha=1-0.99=0.01[/tex]
Two-tailed z-value: [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex] [using z-value table]
[tex]\sigma= 15.2[/tex]
Margin of error : 1 unit.
We assume the population is normally distributed.
Then, the required minimum sample size :-
[tex]n=(\dfrac{(2.576)\cdot15.2}{1})^2[/tex]
Simplify ,
[tex]n=1533.12968704\approx1534[/tex]
∴ Required minimum sample size = 1534
