Answer :
Answer: 10
Step-by-step explanation:
We know that the formula to find the sample size is given by :-
[tex]n= (\dfrac{z_{\alpha/2\cdot \sigma}}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation.
[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex] (significance level)
E= margin of error.
Given : Confidence level : C =99%=0.99
i.e. [tex]1-\alpha=0.99[/tex]
⇒Significance level :[tex]\alpha=1-0.99=0.01[/tex]
By using z-value table ,Two -tailed z-value for [tex]\alpha=0.01 [/tex]:
[tex]z_{\alpha/2}=2.576[/tex]
E= 2 minutes
[tex]\sigma=\text{2.4 minutes}[/tex]
The required sample size will be :-
[tex]n= (\dfrac{2.576\cdot 2.4}{2})^2\\\\= (3.0912)^2\\\\=9.55551744\approx10[/tex]
Hence, the required sample size = 10