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Sagot :
Answer:
[tex]P(x < 2.892) = 4.36\%[/tex]
Step-by-step explanation:
Given
[tex]N = 700[/tex] --- Population
[tex]\mu = 2.894[/tex] -- Mean
[tex]\sigma = 0.009[/tex] --- Standard deviation
[tex]n = 55[/tex] -- Sample
Required: [tex]P(x < 2.892)[/tex]
This question will be solved using the finite correction factor
First, calculated the z score
[tex]z = \frac{x - \mu}{\sqrt{\frac{N -n}{N -1}} * \frac{\sigma}{\sqrt n}}[/tex]
[tex]z = \frac{2.892 - 2.894}{\sqrt{\frac{700 -55}{700 -1}} * \frac{0.009}{\sqrt {55}}}[/tex]
[tex]z = \frac{-0.002}{\sqrt{\frac{645}{699}} * \frac{0.009}{7.42}}[/tex]
[tex]z = \frac{-0.002}{\sqrt{0.92} * \frac{0.009}{7.42}}[/tex]
[tex]z = \frac{-0.002}{0.95917 * 0.0012129}[/tex]
[tex]z = -1.71[/tex]
So:
[tex]P(x < 2.892) = P(z < -1.71)[/tex]
Using z table
[tex]P(x < 2.892) = 0.043633[/tex]
[tex]P(x < 2.892) = 4.36\%[/tex]
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