Sahil Khan
0

  It is given that the weight of 1-year-old girls are normally distributed with an average lifespan of 9.5 kilograms.




Since we have a normal shaped distribution ,and since it is given that the standard deviation is 1.1 kilograms, one standard deviation below the mean is 8.4 kg and one standard deviation above the mean is 10.6 kg as shown below.

Two standard deviations below the mean is 7.3 kg and two standard deviations above the mean is 11.7 kg as shown in the bell curve below.



Three standard deviations below and above the mean are 6.2 kg and 12.8 kg respectively,




According to the empirical rule, 68% of the data lie within 1 standard deviation of the mean, 95% of the data lie within 2 standard deviations of the mean, 99.7% of the data lie within 3 standard deviations of the mean and 0.3% of the data lie outside the 3 standard deviations from the mean. This is shown in the bell curve below.





So, the percentage of 1-year-old girls who are less than 6.2 kg are 0.15%