SAT College

An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 242 to 303 days before the birth of the child, so the pregnancy would have been less than 242 days or more than 303 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father?

1. Calculate the z-scores first, and then use those to calculate the probability. (Round your answer to four decimal places.)

2. What is the probability that he could be the father? (Round your answer to four decimal places.)

Answers

Answer 1

1. The z scores in the question are - 2.92 and 1.769 ,

2. The probability that he is the father = 0.0402

How to solve for the probability

The z score for the 242 days

= 242 - 280 / 13

= -2.92

The z score for the 303 days

= 303 - 280 / 13

= 1.769

The probability that he is not the father

p(242 < x < 303)

p-value ≈ 0.00175 and 0.961553 we would have

0.961553 - 0.00175 = 0.9598

The probability that he is the father is given as 1 - probability that he is not the father.

Hence the probability that he is the father = 1 - 0.9598 = 0.0402

What is probability?

This is the term that is used in mathematics and also in statistics to refer to the likelihood of an event occurring.

The z scores are -2.92 and 1.769 while the calculated probability is 0.0402

Read more on probability here:

https://brainly.com/question/24756209

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Related Questions

Information and knowledge: Which one is obtained from the other?

Answers

Answer:

Information is obtained from knowledge because you can utilize your current knowledge to learn new information.

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