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Answer: [tex]\text{the 80th percentile is 4.898 million cells per microliter \lparen3rd option\rparen}[/tex]Explanation:
Given:
mean = 4.577 million cells per microliter
standard deviation = 0.382 million cells per microliter
To find:
the 80% percentile for the red blood cell counts of women
To determine the 80th percentile, we will apply the z-score formula:
[tex]\begin{gathered} \begin{equation*} z=\frac{X-μ}{σ} \end{equation*} \\ \sigma\text{ = 0.382} \\ \mu\text{ = 4.577} \\ X\text{ = ?} \\ z\text{ = z-score of 80\% percentile} \end{gathered}[/tex][tex]\begin{gathered} Using\text{ z-score percentile for normal distribution} \\ The\text{ z-score of the 80th percentile = 0.842} \end{gathered}[/tex]substitute the values:
[tex]\begin{gathered} 0.842\text{ = }\frac{X-\text{ 4.577}}{0.382} \\ X\text{ - 4.577 = 0.842\lparen0.382\rparen} \\ X\text{ - 4.577 = 0.321644} \end{gathered}[/tex][tex]\begin{gathered} X\text{ - 0.321644 + 4.577} \\ X=\text{ 4.8986} \\ \\ Hence,\text{ the 80th percentile is 4.898 million cells per microliter \lparen3rd option\rparen} \end{gathered}[/tex]
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