A normal distribution has a mean of µ = 40 with σ = 10.What proportion of the scores in this distribution are greater than X = 55?
A)0.3085
B)0.6915
C)0.0668
D)0.9332

Question

A normal distribution has a mean of µ = 40 with σ = 10.What proportion of the scores in this distribution are greater than X = 55?​
A)​0.3085
B)​0.6915
C)​0.0668
D)​0.9332

Quizplus · Accepted Answer

We can use the standard normal distribution by transforming X into a z-score:

z = (X - µ) / σ = (55 - 40) / 10 = 1.5

Then, we can use a z-table or calculator to find the proportion of scores greater than z = 1.5:

P(z > 1.5) = 1 - P(z < 1.5) = 1 - 0.9332 = 0.0668

Therefore, the proportion of scores greater than X = 55 is 0.0668 or approximately 6.68%. Choice C is the correct answer.

A Normal Distribution Has a Mean of µ = 40