A study studied the birth weights of 1,278 babies born in the united states. the mean weight was 3234 grams with a standard deviation of 871 grams. assume that birth weight data are approximately bell-shaped. estimate the number of newborns who weighed between 1492 grams and 4976 grams.

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Mckinley Clark

Mathematics

26 July, 23:39

A study studied the birth weights of 1,278 babies born in the united states. the mean weight was 3234 grams with a standard deviation of 871 grams. assume that birth weight data are approximately bell-shaped. estimate the number of newborns who weighed between 1492 grams and 4976 grams.

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Daniel Bush · Answer 1

1220 Subtracting the lower boundary of 1492 grams from the mean of 3234 gives you 1742 grams below the mean. Dividing 1742 by the standard deviation of 871 gives you 2 standard deviations below the curve. Now doing the same with the upper limit of 4976 grams also gives you 2 standard deviations above the mean (4976-3234) / 871 = 2 So you now look for what percentage of the population lies within 2 standard deviations of the mean. Standard lookup tables will indicate that 95.4499736% of the population will be within 2Ď of the mean. So multiply 1278 by 0.954499736 giving 1219.851. Then round to the nearest whole number and you have an estimated 1220 babies that weigh between 1492 grams and 4976 grams.