We appreciate your visit to Jonah is reviewing the final exam scores of the previous year s graduates in the Engineering program from which he is about to graduate The. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We begin by noting that the final exam scores are normally distributed with a mean of [tex]$\mu = 70$[/tex] and a standard deviation of [tex]$\sigma = 4$[/tex]. To determine Jonah's standing in percentiles, we first calculate the [tex]$z$[/tex]-score corresponding to his score of 78. The [tex]$z$[/tex]-score is given by
[tex]$$
z = \frac{x - \mu}{\sigma},
$$[/tex]
where [tex]$x$[/tex] represents Jonah's score. Substituting the given values, we have
[tex]$$
z = \frac{78 - 70}{4} = \frac{8}{4} = 2.
$$[/tex]
Next, we use the standard normal distribution to find the cumulative probability corresponding to [tex]$z = 2$[/tex]. This cumulative probability tells us the fraction of students who scored below Jonah's score. For [tex]$z = 2$[/tex], the cumulative probability is approximately 0.97725. Converting this into a percentage, we get
[tex]$$
0.97725 \times 100 \approx 97.7\%.
$$[/tex]
Thus, Jonah's score of 78 places him in the 97.7th percentile.
The correct answer is hence [tex]$\boxed{97.7\%}$[/tex].
[tex]$$
z = \frac{x - \mu}{\sigma},
$$[/tex]
where [tex]$x$[/tex] represents Jonah's score. Substituting the given values, we have
[tex]$$
z = \frac{78 - 70}{4} = \frac{8}{4} = 2.
$$[/tex]
Next, we use the standard normal distribution to find the cumulative probability corresponding to [tex]$z = 2$[/tex]. This cumulative probability tells us the fraction of students who scored below Jonah's score. For [tex]$z = 2$[/tex], the cumulative probability is approximately 0.97725. Converting this into a percentage, we get
[tex]$$
0.97725 \times 100 \approx 97.7\%.
$$[/tex]
Thus, Jonah's score of 78 places him in the 97.7th percentile.
The correct answer is hence [tex]$\boxed{97.7\%}$[/tex].
Thanks for taking the time to read Jonah is reviewing the final exam scores of the previous year s graduates in the Engineering program from which he is about to graduate The. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
