Question

To study bonding between mothers and infants, a researcher places each mother and her infant in a playroom and has the mother leave for 10 minutes. The researcher records crying time in the sample of infants during this time that the mother was not present and finds that crying time is normally distributed with

M = 8

and

SD = 1.1.

Based on the empirical rule, state the range of crying times within 68% of infants cried, 95% of infants cried, and 99.7% of infants cried.

(a) 68% of infants cried
__________ to __________ min

(b) 95% of infants cried
  _______ to ________min

(c) 99.7% of infants cried
  _________ to _________ min

Answer 1

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule can be broken down into three parts:

• 68% of data falls within the first standard deviation from the mean.
• 95% fall within two standard deviations.
• 99.7% fall within three standard deviations.

The rule is also called the 68-95-99 7 Rule or the Three Sigma Rule.

Given

mean =

standard deviation =

a)

According to empirical rule, 68% of the data falls within one standard deviation of the mean.

i.e.

(8 - 1.1 , 8 + 1.1 )

( 6.9 , 9.1 )

Therefore, 68% of infants cried 6.9 to 9.1 min.

b)

According to empirical rule, 95% of the data falls within two standard deviation of the mean.

i.e.

(8 - 2.2 , 8 + 2.2 )

( 5.8 , 10.2 )

Therefore, 95% of infants cried 5.8 to 10.2 min.

c)

According to empirical rule, 99.7% of the data falls within three standard deviation of the mean.

i.e.

(8 - 3.3 , 8 + 3.3 )

( 4.7 , 11.3 )

Therefore, 99.7% of infants cried 4.7 to 11.3 min.