Step 1
Find the Z-score
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ \sigma=6.57 \\ x=236 \\ \mu=246 \end{gathered}[/tex][tex]\begin{gathered} Z=\frac{236-246}{6.57} \\ Z=\frac{-10}{6.57}=\frac{-1000}{657} \end{gathered}[/tex]
Step 2
Find the probability that 49 balls traveled less than 236ft
[tex]\begin{gathered} P(x<236)=\text{ P\lparen z<}\frac{-1000}{657}) \\ \text{P\lparen z<}\frac{-1000}{657})=0.0639957691005 \\ \text{P\lparen z<}\frac{-1000}{657})\approx0.0640 \end{gathered}[/tex]
Step 3
Find the 80th percentile of the distribution of the average of 49 fly balls.
Let the 80th percentile of the distribution of 49 fly balls be a
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