An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of days and a standard deviation of days. An alleged father was out of the country from to days before the birth of the child, so the pregnancy would have been less than days or more than 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? What is the probability that he could be the father? Calculate the localid="1653472319552" -scores first, and then use those to calculate the probability.
His probability of being the father is .
Let variable has normal distribution with mean localid="1653469397337" and variance . Then probability density function is defined by:
The localid="1653469465424" statistic for value is calculated as follows:
If statistic is positive, value is standard deviation to the right of the mean, whereas statistic is negative, the value is standard deviation to the left of the mean.
The length of a pregnancy in this task has a normal distribution with a mean of and a standard deviation of days. Now we must determine the likelihood that this individual is not a father, followed by the likelihood that he is a father. We must first locate the statistics for the days and days. We have:
We'll utilise these numbers to figure out whether he's the father or not. We'll start by calculating the odds that he isn't the father. Let's define the variable , which represents the length of pregnancy, and then write . We need to find the likelihood that standardizing variable is between and to calculate that he is not the father. Now we have:
The probability that he is not the father is . We must now determine the likelihood that he is a parent. We must calculate the probability that the standardize variable is smaller than and greater than . Now we have:
Terri Vogel, an amateur motorcycle racer, averages seconds per mile lap (in a seven-lap race) with a standard deviation of seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.
a. In words, define the random variable .
c. Find the percent of her laps that are completed in less than seconds.
d. The fastest of her laps are under
e. The middle of her laps are from seconds to seconds.
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