Answer:
a) 166
Step-by-step explanation:
Explanation:-
Step 1:-
maximum Error of estimation (E) =1.2
we know that maximum Error of estimation
[tex]E = \frac{S.D )z\alpha }{\sqrt{n} }[/tex]
cross multiplication we get ,
E(√n) =σ (zₐ)
Squaring on both sides, we get
[tex]n =( \frac{z_{\alpha }S.D }{E} )^{2}[/tex]
Step 2:-
Population of standard deviation σ = 6
level of significance ∝ = 2.576 at 99% of confidence interval
By using formula
[tex]n =( \frac{z_{\alpha }S.D }{E} )^{2}[/tex]
substitute all values in above equation
[tex]n =(\frac{2.576 X6}{1.2})^2[/tex]
on simplification , we get n = 165.8 ≅166
Conclusion:-
confidence level 99% requires a sample size of at least (n)=166
