Question

# the quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to...

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?

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

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