1.) If a variable has a distribution that is bell-shaped with mean 26 and standa

Question

1.) If a variable has a distribution that is bell-shaped with mean 26 and standard deviation 4, then according to the Empirical Rule, what percent of the data will lie between 18 and 34?

2.) If a variable has a distribution that is bell-shaped with mean 16 and standard deviation 5 then according to the Empirical Rule, 68.0% of the data will lie between which values?

According to the Empirical Rule, 68.0% of the data will lie between ____ and ____

3.) The standard deviation is a resistant measure of spread. TRUE OR FALSE?

Explanation / Answer

1. As per the Empirical rule, 95% of the data lies between two standard deviations from the mean.

Here,

Range of 2 SD = (26 - 2*4, 26 +2*4) = (18, 34)

Hence,

Percent of data that will lie between 18 and 34 = 95%

2. As per Empirical rule, 68% data lies between 1 SD from the mean.

Hence,

According to the Empirical Rule, 68.0% of the data will lie between (16 - 5) and (16 + 5) i.e. between 11 and 21.

3. False

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