Question

Central Limit Theorem: Finding

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Value The lengths of pregnancies in a small rural village are normally distributed with a mean of 264 days and a standard deviation of 13 days. In what range would you expect to find the middle 50% of most pregnancies?

Answer 1

To determine the probability of paternity based on pregnancy length, z-scores for a normal distribution with a given mean and standard deviation are calculated, and corresponding probabilities are derived from a standard normal distribution table.

Step-by-step explanation:

The goal of this problem is to calculate the probability that a given male animal could be the father to an offspring based on the duration of the pregnancy. Since the length of the pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days, we can use z-scores to find the probabilities required.

First, we calculate the z-scores for both the minimum and maximum lengths of pregnancy that would indicate the male animal could be the father (less than 240 days or more than 306 days). For a pregnancy less than 240 days, the z-score is (240 - 280) / 13. For a pregnancy more than 306 days, the z-score is (306 - 280) / 13.

Using the corresponding z-score values, we can look up the probabilities in a standard normal distribution table or use a calculator provided these values to get the probabilities that the male animal was not the father, and consequently the probability that he could be the father by subtracting from 1.