Answer :
Answer:
E. 85
Step-by-step explanation:
We have been given that a Statistics teacher decides to give A's only to students who score in the top 15% on the final exam. The scores are normally distributed with a mean of 78 and a standard deviation of 7 (this is also the population standard deviation).
We will use normal distribution table and z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z= Z-score,
x = Sample score,
[tex]\mu=\text{Mean}\\\sigma=\text{Standard deviation}[/tex]
[tex]z=\frac{x-78}{7}[/tex]
We know that top 15% means 85% and more.
Let us find z-score corresponding to 85% or 0.85 using normal distribution table.
[tex]1.04=\frac{x-78}{7}[/tex]
Let us solve for x.
[tex]1.04*7=\frac{x-78}{7}*7[/tex]
[tex]7.28=x-78[/tex]
[tex]7.28+78=x-78+78[/tex]
[tex]85.28=x[/tex]
[tex]x\approx 85[/tex]
Therefore, the lowest score, a student could earn and still receive an A, is 85 and option E is the correct choice.