Question

question 3 suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points. suppose that the top 4% of the exams will be given an a+. in order to be given an a+, an exam must earn at least what score? report your answer in whole numbers.

Explanation:

Step1: Find z - score for top 4%

The top 4% means an area of 0.96 to the left. Looking up in z - table, $z\approx1.75$.

Step2: Use z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$. Rearranging for $x$ gives $x = \mu+z\sigma$. Substituting $\mu = 75$, $z = 1.75$, and $\sigma = 8$, we get $x=75 + 1.75\times8$.

Step3: Calculate x

$x=75+14 = 89$.

Answer:

89