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Normal Distribution and Birth Weights

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A researcher recorded the birth weights of a sample of newborn babies. The average birth weight was 7.2 pounds and the standard deviation was 0.9 pound. The birth weights follow a normal distribution.

1. Label the number line so that the curve is a normal curve and follows the properties of the normal distribution. Include 3 standard deviations above and below the mean.
2. Determine the percent of newborns that weight between 2 standard deviations below the mean and 2 standard deviations above the mean.
3. Determine the percent of newborns that weight less than the mean.
4. Determine the percent of newborns that weight between 1 standard deviation above the mean and 3 standard deviations above the mean.
5. Approximately what percent of newborns weighed between 4.5 pounds and 9.9 pounds?
6. Approximately what percent of newborns weight more than 9 pounds?
7. Approximately what percent of newborns weighed less than 6.3 pounds?

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The Solution identifies by standard deviation the percentages of newborn babies based on their average birth weight. Explanations are given for the solutions. Step-by-step computations are shown.

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A researcher recorded the birth weights of a sample of newborn babies. The average birth weight was 7.2 pounds and the standard deviation was 0.9 pound. The birth weights follow a normal distribution.
1. Label the number line so that the curve is a normal curve and follows the properties of the normal distribution. Include 3 standard deviations above and below the mean.

Repeatedly add 0.9 to 7.2 to get the numbers on the right side of the graph.
Repeatedly subtract 0.9 from 7.2 to get the number on ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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