Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
ANSWER
[tex]71.56[/tex]EXPLANATION
Parameters given:
Mean, μ = 64
Standard deviation, σ = 9
To find the cutoff score, we want to find the score that has a corresponding z-score which represents the top 20% of the data.
To do this, first, we have to subtract 20% from 100%:
[tex]\begin{gathered} 100-20 \\ \Rightarrow80\% \end{gathered}[/tex]Now, we have to use the standard normal table to find the z score that corresponds to the closest value to 80% (0.80) on the standard normal table i.e. P(x > 80).
From the table, we see that the z-score that corresponds to 0.80 (0.79955 from the table) is 0.84.
Now, using the formula for z-score, find the cutoff score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = cutoff score
Solving for x, we have that:
[tex]\begin{gathered} 0.84=\frac{x-64}{9} \\ \Rightarrow0.84\cdot9=x-64 \\ \Rightarrow x-64=7.56 \\ \Rightarrow x=64+7.56 \\ x=71.56 \end{gathered}[/tex]That is the cutoff score.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
