A normal distribution has a mean of µ = 24 with σ = 3.What is the minimum score needed to be in the top 14% of the distribution?
A)X = 24.42
B)X = 25.08
C)X = 27.24
D)X = 20.76

Question

Quizplus · Accepted Answer

To find the minimum score needed to be in the top 14% of a normal distribution, we use the Z-score formula and look up the Z-score that corresponds to the top 14% in a standard normal distribution table or use a calculator. The Z-score for the top 14% (or 86th percentile since 100% - 14% = 86%) is approximately 1.08. Using the Z-score formula $Z = \frac{X - \mu}{\sigma}$, where $\mu = 24$ and $\sigma = 3$, and solving for $X$ gives us $X = \mu + Z\sigma = 24 + 1.08(3) = 24 + 3.24 = 27.24$.

A Normal Distribution Has a Mean of µ = 24