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 = 20.76
B)X = 27.24
C)X = 25.08
D)X = 24.42

Question

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 = 20.76
B)​X = 27.24
C)​X = 25.08
D)​X = 24.42

Quizplus · Accepted Answer

To find the minimum score in the top 14% of the distribution, we need to find the z-score that corresponds to the 86th percentile (100% - 14%). Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 86th percentile is approximately 1.08. 
Now we can use the formula: 
z = (X - µ) / σ 
where X is the minimum score we want to find. Rearranging, we get: 
X = z*σ + µ 
Plugging in the values, we get: 
X = 1.08*3 + 24 = 27.24 
Therefore, the minimum score needed to be in the top 14% of the distribution is 27.24, which corresponds to choice B.

A Normal Distribution Has a Mean of µ = 24