Answer:
[tex]P(p>0.43) = 0.0436[/tex]
Step-by-step explanation:
Given
[tex]p = 40\%[/tex] -- proportion of baseball players
[tex]n = 781[/tex] --- selected sample
Required
Determine P(p>43%)
First, calculate the z score using:
[tex]Z = \frac{\^{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
This gives:
[tex]Z = \frac{48\%-40\%}{\sqrt{\frac{40\% *(1 - 40\%)}{781}}}[/tex]
Convert % to decimal
[tex]Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *(1 - 0.40)}{781}}}[/tex]
[tex]Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *0.60}{781}}}[/tex]
[tex]Z = \frac{0.43-0.40}{\sqrt{\frac{0.24}{781}}}[/tex]
[tex]Z = \frac{0.03}{\sqrt{0.00030729833}}[/tex]
[tex]Z = \frac{0.03}{0.01752992669}[/tex]
[tex]Z = 1.71[/tex]
So:
[tex]P(p>0.43) = P(Z>1.71)[/tex]
[tex]P(p>0.43) = 1 - P(Z<1.71)[/tex]
[tex]P(p>0.43) = 1 - 0.9564[/tex]
[tex]P(p>0.43) = 0.0436[/tex]
