A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 55, what proportion of the scores are on the right side of the line?

The proportion of the scores that are on the right side of the line is 0.0668

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

µ of a normal distribution = 40

σ of a normal distribution = 10

X = 55

2. What proportion of the scores are on the right side of the line?

Let's calculate the z-score for X = 55, this way:

z-score = (X - µ) / σ

z-score = (55 - 40) / 10

z-score = 1.5

Now, using the z-table, let's calculate the proportion, this way:

p (z = 1.5) = 0.9332

In consequence,

p (z > 1.5) = 1 - 0.9332 = 0.0668