Babies’ birth weights are approximately normally distributed with mean 3375 gram

Question

Babies’ birth weights are approximately normally distributed with mean 3375 grams and standard deviation 493 grams. An obstetrician wants to conduct a study of babies that are unusually heavy or unusually light, to try to understand what genetic and nutritional factors might contribute to this. He decides that babies with weights in the top 2.5% will be considered unusually heavy, and babies with weights in the bottom 2.5% will be considered unusually light.

Babies that weigh more than ___ grams or less than ___ grams will be included in the study.

Explanation / Answer

adding up the top 2.5% which will be considered unusually heavy, and babies with weights in the bottom 2.5% will be considered unusually light. the remaining is 1-5% or 95%

also the z value for 95% confidence is 1.96

thus lower value is mean-z*s=3375-493*1.96=2408.72

higher value is mean+z*s=3375+493*1.96=4341.28

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