Question

The heights of newborn babies have a symmetric distribution with a mean of 20 inches and a SD of 2 inches. Find the percentage of newborn babies whose height is between 18 inches and 22 inches

Answer the following questions:

• Do you apply Chebyshev’s Theorem or OR Empirical Rule?
• What is K? Remember that “k” is the number of standard deviation from the mean?
• The percentage of newborn babies whose height is between 18 inches and 22 inches is:

Answer 1

Solution:

Given a Symmetric shaped distribution( NORMAL DISTRIBUTION) with

= 45

= 6

When distribution is symmetric , we use Empirical rule. Otherwise use Chebyshev's Theorem.

Now ,

18 = 20 - 2 = - 1

22 = 20 + 2 = + 1

So , k = 1

According to the empirical rule , 68% of the data lie within 1 standard deviations from the mean

i.e. between - and +

The percentage of newborn babies whose height is between 18 inches and 22 inches is: 68 %