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Chapter 3: Problem 36

Distributions of gestation periods (lengths of pregnancy) for humans are roughly bell-shaped. The mean gestation period for humans is 272 days, and the standard deviation is 9 days for women who go into spontaneous labor. Which is more unusual, a baby being born 9 days early or a baby being born 9 days late? Explain.

Short Answer

Expert verified
Both scenarios, a baby being born 9 days early and a baby being born 9 days late, are equally unusual as they are both 1 standard deviation away from the mean in a bell curve or normal distribution. Thus, they have equal probabilities of occurrence.

Step by step solution

01

Understanding Normal Distribution

In the normal distribution or the bell-shaped curve, the mean represents the highest point in the curve or the peak, which implies it's the most occurring value. The standard deviation indicates the dispersion or how spread out the values are from the mean. Any value within 1 standard deviation from the mean is considered typical or usual.
02

Early Birth Scenario

A baby being born 9 days early is considered as 272 days - 9 days = 263 days. This is 1 standard deviation below the mean. In a normal distribution, approximately 84% of all values lie below this point.
03

Late Birth Scenario

A baby being born 9 days late is considered as 272 days + 9 days = 281 days. This is 1 standard deviation above the mean. In a normal distribution, approximately 16% of all values lie above this point and 84% lie below.
04

Comparing the Scenarios

Putting our analysis into perspective, both scenarios are equally distant from the mean (9 days), but in opposite directions. Because they are both 1 standard deviation from the mean, they are equally likely as per the properties of the normal distribution. Namely, as much as the curve is to the left of the mean, so it is to the right and vice versa.

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Most popular questions from this chapter

In 1994, Major League Baseball (MLB) players went on strike. At the time, the average salary was \(\$ 1,049,589\), and the median salary was \(\$ 337,500\). If you were representing the owners, which summary would you use to convince the public that a strike was not needed? If you were a player, which would you use? Why was there such a large discrepancy between the mean and median salaries? Explain. (Source: www.usatoday.com)

This list represents the number of children for the first six "first ladies" of the United States. (Source: 2009 World Almanac and Book of Facts) $$ \begin{array}{ll} \text { Martha Washington } & 0 \\ \text { Abigail Adams } & 5 \\ \hline \text { Martha Jefferson } & 6 \\ \text { Dolley Madison } & 0 \\ \text { Elizabeth Monroe } & 2 \\ \hline \text { Louisa Adams } & 4 \end{array} $$ a. Find the mean number of children, rounding to the nearest tenth. Interpret the mean in this context. b. According to eh.net/encyclopedia, women living around 1800 tended to have between 7 and 8 children. How does the mean of these first ladies compare to that? c. Which of the first ladies listed here had the number of children that is farthest from the mean and therefore contributes most to the standard deviation? d. Find the standard deviation, rounding to the nearest tenth.

Is it possible for a standard deviation to be negative? Explain.

Earnings A sociologist says, "Typically, men in the United States still earn more than women." What does this statement mean? (Pick the best choice.) a. All men make more than all women in the United States. b. All U.S. women's salaries are less varied than all men's salaries. c. The center of the distribution of salaries for U.S. men is greater than the center for women. d. The highest-paid people in the United States are men.

Four siblings are \(2,6,9\), and 10 years old. a. Calculate the mean of their current ages. Round to the nearest tenth. b. Without doing any calculation, predict the mean of their ages 10 years from now. Check your prediction by calculating their mean age in 10 years (when they are \(12,16,19\), and 20 years old). c. Calculate the standard deviation of their current ages. Round to the nearest tenth. d. Without doing any calculation, predict the standard deviation of their ages 10 years from now. Check your prediction by calculating the standard deviation of their ages in 10 years. e. Adding 10 years to each of the siblings ages had different effects on the mean and the standard deviation. Why did one of these values change while the other remained unchanged? How does adding the same value to each number in a data set affect the mean and standard deviation?
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