Question

Scores on the Common final exam in Stat 1222 course are randomly distributed with mean 75 and Standard deviation 5. The department decides to give A to all students whose scores are in the top 10% on this exam.
What is the minimum score for a student to receive A?

Answer 1

Answer:

The minimum score for a student to receive A is 81.4.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 75, \sigma = 5$

The department decides to give A to all students whose scores are in the top 10% on this exam.

What is the minimum score for a student to receive A?

The minimum score is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 75}{5}$

$X - 75 = 1.28*5$

$X = 81.4$

The minimum score for a student to receive A is 81.4.