A normal distribution has a mean of µ = 40 with σ = 10.What proportion of the scores in this distribution are smaller than X = 35?
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 smaller than X = 35?​
A)​0.3085
B)​0.6915
C)​0.0668
D)​0.9332

Quizplus · Accepted Answer

To find the proportion of scores smaller than X = 35 in a normal distribution with a mean (µ) of 40 and a standard deviation (σ) of 10, we calculate the Z-score for X = 35. The Z-score formula is Z = (X - µ) / σ = (35 - 40) / 10 = -0.5. Looking up the Z-score of -0.5 in a standard normal distribution table or using a calculator, we find the proportion of scores below this Z-score is approximately 0.3085.

A Normal Distribution Has a Mean of µ = 40