Answer:
The sample must be greater than 55
Step-by-step explanation:
Confidence = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The z score of α/2 (0.005) corresponds to the z score of 0.495 (0.5 - 0.005) which is equal to 2.576
[tex]z_\frac{\alpha}{2} =2.576[/tex]
The margin of error (E) is given by the formula:
[tex]E=z_\frac{\alpha}{2}*\sqrt{\frac{\sigma^2}{n} }\\ \\n=sample\ size,\sigma=standard\ deviation,\sigma^2=variance\\\\Given\ that:\\\\\sigma^2=10000,E=35,z_\frac{\alpha}{2}=2.576\\\\35= 2.576*\sqrt{\frac{10000}{n} }\\\\35= 2.576*\frac{100}{\sqrt{n} } \\\\35= \frac{257.6}{\sqrt{n} }\\\\\sqrt{n} =\frac{257.6}{35 }\\\\\sqrt{n} =7.36\\\\n=7.36^2\\\\n=54.17[/tex]
n > 55
The sample must be greater than 55 so that the margin of error will not exceed 35 hours
