Question

Last week, Sarah had exams in math and in Spanish. On the math exam, the mean was µ = 30 with Ï = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with Ï = 8, and Sarah had a score of X = 68. For which class should Sara expect the better grade?
A. There is not enough information to determine which is the better grade.
B. Spanish
C. Math
D. The grades should be the same because the two exam scores are in the same location.

Answer 1

Answer:

For which class should Sara expect the better grade?

C. Math

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

For this case we can use the z score formula in order to find the position and the probability would represent the percentile for each case.

Math Exam

$X \sim N(\mu=30,\sigma=5)$

$z= \frac{45-30}{5}=3$

$P(X<45)=P(Z<3) =0.99865$

So the score is on the 99 percentile approximated.

Spanish Exam

$X \sim N(\mu=60,\sigma=8)$

$z= \frac{68-60}{8}=1$

$P(X<68)=P(Z<1) =0.84134$

So the score is on the 84 percentile approximated.

So we can see that the percentile is higher for the Math class so then the best answer would be:

For which class should Sara expect the better grade?

C. Math