Math Problem Statement
The gestation time (the time elapsed between conception and birth) for pregnancies without problems in humans is approximately normally distributed with a mean of 266 days and a standard deviation of 16 days. 1 What percentage of pregnancies last between 234 and 298 days? 2 In a paternity case, a woman claims her pregnancy lasted 312 days. The supposed father of the child had been sent away on a scientific expedition to Antarctica 312 days before the birth. What percentage of gestation times exceed 312 days in length? 3 Suppose that 100 chosen women give birth one day at a hospital. What is the probability, to four decimal places, that at least one of the women has a gestation period of more than 312 days in length? 4 Find, to the nearest day, the length of gestation that is exceeded by only 5% of pregnancies.
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Z-score
Probability
Formulas
Z-score formula: Z = (X - μ) / σ
Theorems
Properties of Normal Distribution
Suitable Grade Level
Grades 10-12
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