Question

the quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to answer the following: A qunatitative data set of size 70 has mean 40 and standard deviation 2. Approximately how many observations lie between 34 and 46?

Answer 1

the dataset has

we will find how many standard deviations are 34 and 46 away from the mean

for 34

for 46

These scores are 3 standard deviation away from the mean and using empirical rule

The Empirical Rule states that states that

68% of the data falls within one standard deviation.

95% of the data lies within two standard deviations.

Within three standard deviations is 99.7% ( almost all) of the data.

total number of observations that lie between 34 and 46 is 70*0.997=69.79 observations round off to integer it will be 70