If a distribution is normal with μ = 50 and σ = 10, then what proportion of the scores will fall between 40 and 60?
A).1359
B).3413
C).6826
D).9544

Question

Quizplus · Accepted Answer

We can use the empirical rule, which states that for a normal distribution:
-68% of the data falls within one standard deviation of the mean
-95% of the data falls within two standard deviations of the mean
-99.7% of the data falls within three standard deviations of the mean

Since we are looking for the proportion of scores between 40 and 60, we need to find how many standard deviations away from the mean these values are:
z-score for 40: (40-50)/10 = -1
z-score for 60: (60-50)/10 = 1

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean (z-scores between -1 and 1). Therefore, approximately 68/2 = 34% of the data falls between 40 and 60. This is equal to 0.34 or 34% in decimal form, or 0.3400 when rounded to four decimal places. This is closest to answer choice C), 6826.

If a Distribution Is Normal with μ = 50 and σ