Answer:
The Sample size is 1918.89035
Step-by-step explanation:
Consider the provided information.
It is given that 14 out of 105 samples failed.
Therefore p = 14/105 = 0.13 3... and q=1-0.133=0.867
Samples would be needed to create a 99 percent confidence interval.
Subtract the confidence level from 1, then divide by two.
[tex]\frac{(1 -0.99)}{2}=0.005[/tex]
By standard normal table z=2.5758≈2.58
Calculate the sample size as:
[tex]n=\frac{z^2pq}{e^2}[/tex]
Where, e is the margin of error,
Substitute the respective values.
[tex]n=\frac{(2.58)^2(0.133)(0.867)}{(0.02)^2}=1918.89[/tex]
Hence, the Sample size is 1918.89035