Question

The weights of adult male beagles are normally distributed with a mean, ? = 25 pounds and a standard deviation, ? = 3 pounds.

a. Use the empirical rule to find the percentage of beagles that weigh between 22 and 28 pounds. %

b. Use the empirical rule to find the percentage of beagles that weigh between 19 and 31 pounds

Answer 1

Emperical rule (68-95-99.7) states that,

About 68% data falls in 1 standard deviation of the mean.

About 95% data falls in 2 standard deviation of the mean.

About 99.7% data falls in 3 standard deviation of the mean.

a)

We have to calculate P( 22 < X < 28) = ?

We can write 22 in terns of and as

22 = 25 - 3

= - 1 *

That is 22 is 1 standard deviation below the mean.

Sinmilarly,

28 = 25 + 1 * 3

= + 1 *

That is 28 is 1 standard deviation above the mean.

Hence, 22 and 28 are 1 standard deviation of the mean.

By the emperical rule,

P(22 < X< 28) = 68%

b)

We can write 19 as

19 = 25 - 2 * 3

= - 2 *

That is 19 is 2 standard deviation below the mean.

Similarly,

31 = 25 a and + 2 * 3

= + 2 *

That is 31 is 2 standard deviation above the mean.

Hence, 19 and 31 are 2 standard deviation of the mean.

By the emperical rule,

P( 19 < X < 31) = 95%