Respuesta :
Answer:
The minimum score you have to make on the final exam to be in the top 10% of students and guarantee yourself an A is 88.3 points.
Step-by-step explanation:
We are given that the ENGR/PHYS 216 faculty have a final exam grade distribution that is, miraculously, exactly a normal distribution.
Last year, the final exam average was 78 with a standard deviation of 8 points.
Let X = final exam grade distribution
SO, X ~ Normal([tex]\mu=78,\sigma^{2} =8^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 78 points
[tex]\sigma[/tex] = standard deviation = 8 points
Now, the minimum score we have to make on the final exam to be in the top 10% of students and guarantee yourself an A is given by;
P(X > x) = 0.10 {where x is required minimum score}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-78}{8}[/tex] ) = 0.10
P(Z > [tex]\frac{x-78}{8}[/tex] ) = 0.10
Now, in the z table the critical value of X which represents the top 10% of the probability area is given as 1.282, that means;
[tex]\frac{x-78}{8}[/tex] = 1.282
x - 78 = [tex]1.282 \times 8[/tex]
x = 78 + 10.26 = 88.3 points
Hence, the minimum score you have to make on the final exam to be in the top 10% of students and guarantee yourself an A is 88.3 points.
