Question

If a variable has a distribution that is? bell-shaped with mean 23 and standard deviation 3?, then according to the Empirical? Rule, what percent of the data will lie between 14 and 32??

Answer 1

According to emperical rule(68 - 95 - 99.7)

Approximately, 68% of the data lie in 1 standard deviation of the mean.

Approximately, 95% of the data lie in 2 standard deviation of the mean.

Approximately, 99.7% of the data lie in 3 standard deviation of the mean.

We have to calculate P( 14 < X < 32) = ?

Now,

14 = 23 - 3 * 3

14 = Mean - 3 * SD

That is 14 is 3 standard deviation below the mean.

Similarly,

32 = 23 + 3 * 3

32 = Mean + 3 * SD

32 is 3 standard deviation above the mean.

That is 14 and 32 are 3 standard deviation of the mean.

Accrding to emperical rule,

99.7% data lie between 14 and 32.