A normal distribution has a mean of µ = 80 with σ = 20.What score separates the lowest 30% of the distribution from the rest of the scores?
A)X = 90.4
B)X = 69.6
C)X = 110
D)X = 50

Question

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the lowest 30% of the distribution from the rest of the scores?​
A)X = 90.4​
B)​X = 69.6
C)​X = 110
D)​X = 50

Quizplus · Accepted Answer

Using a standard normal distribution table or calculator, we can find the z-score that separates the lowest 30% of the distribution. The z-score corresponding to a cumulative probability of 0.30 is approximately -0.52. We can then use the formula z = (X - μ) / σ to find the corresponding X value: -0.52 = (X - 80) / 20, which gives X = 69.6. Therefore, the score that separates the lowest 30% of the distribution is X = 69.6.

A Normal Distribution Has a Mean of µ = 80