Use the Empirical Rule to answer the questions below: The distribution of weight
ID: 3371711 • Letter: U
Question
Use the Empirical Rule to answer the questions below:
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.3 pounds and a standard deviation of 0.6 pounds.
Explanation / Answer
a) 7.9 = 7.3 + 0.6 that is one standard deviation above mean
According to empirical rule of normal distribution, 68% of the observations lies within one standard deviation from the mean that is 32% lies outside that range which means 32/2 = 16% of the observations lies one either side outside the range.
Therefore 0.16 is the required probability here.
b) According to the empirical rule of normal distribution, 95% of the distribution values lies within 2 standard deviations from the mean. Therefore, here they lie between 7.3 - 2*0.6 = 6.1 and 7.3 + 2*0.6 = 8.5
c) 6.1 = 7.3 - 2*0.6
95% lies within 2 standard deviations from the mean. Therefore 5% lies outside and 5/2 = 2.5% lies outside 2 standard deviations and on either side.
Therefore 2.5% is the required answer here.
d) Approximately 50% observations are more than the mean that is 7.3 pounds
e) 6.7 = 7.3 - 0.6 Therefore 16% lies less than 6.7
9.1 = 7.3 + 3*0.6
now 99.7% lies within 3 standard deviations of the mean that is 0.3/2 = 0.15% lies outside 3 standard deviations on either side.
Therefore required percentage here is computed as: = 100 - 16 - 0.15 = 83.85% of the observations
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