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 the z - score

We know that the top 4% of the data means the area to the right of the z - score is 0.04. So the area to the left is $1 - 0.04=0.96$. Looking up in the standard normal distribution table, the z - score corresponding to an area of 0.96 is approximately $z = 1.75$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 75$, $\sigma = 8$, and $z = 1.75$. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate the score

Substitute the values into the formula: $x = 75+1.75\times8$. First, calculate $1.75\times8 = 14$. Then $x=75 + 14=89$.

Answer:

89