Section: Module 2: Lesson 2: Variables, Sampling, and Distribution | Biostatistics | NextGenU.org
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Learning Objectives
- Understand the concept of random variables.
- Distinguish between samples and population and identify different types of samples.
- Understand sampling distribution, variance, and the central limit theorem.
- Understand the implications and uses of normality and skewness.
- Be able to calculate and correctly interpret probability data from a sampling distribution.
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Students mustView
- Read the entire web page.
- Understand the concept of random variables.
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Students mustView
- Read the entire web page. Attempt any questions if understanding is weak.
- Distinguish between samples and population and identify different types of samples.
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Students mustView
- Read the entire web page.
- Distinguish between samples and population and identify different types of samples.
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Students mustView
- Read the entire chapter (pages 19–60). Focus on sections 3.1, 3.4, 3.5, 3.7, 3.8, and 3.9.
- Understand sampling distribution, variance, and the central limit theorem.
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Students mustView
- Read the web page. Then, access the lesson "Sampling Distribution of the Mean" by clicking on the link titled "Standard" found on the left side of the web page under the heading "6. Sampling Distribution of the Mean" in the section titled "Chapter IX. Sampling Distribution". Read the content of that link.
- Understand sampling distribution, variance, and the central limit theorem.
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Students mustView
- Read the entire web page.
- Understand sampling distribution, variance, and the central limit theorem.
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Students mustView
- Read the entire article.
- Understand sampling distribution, variance, and the central limit theorem.
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Students mustView
- Read the web page, as well as the next two web pages, "1.5.2 – Measures of Position" and "1.5.3 – Measures of Variability". Access lessons 1.5.2 and 1.5.3 by either clicking on the link found on the left side of the web page under the heading "Lesson 1" or by clicking on the links "1.5.2 – Measures of Position" and "1.5.3 – Measures of Variability" found at the end of the text on the bottom right-hand side of the web page.
- Understand the implications and uses of normality and skewness.
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Students mustMark as done
- Data on newborns, such as gestational age and birthweight, can be helpful in establishing baseline health statuses for maternal and infant health. Premature births and low birthweights can be detrimental to an infant’s development. For Mexican-American infants born in the state of Arizona in 1986 and 1987, the probability that an infant’s gestational age is less than 37 weeks is 0.142 and the probability that his or her birthweight is less than 2,500 grams is 0.051. Furthermore, the probability that these two events occur simultaneously is 0.031.
- Let A be the event that an infant’s gestational age is less than 37 weeks and B the event that his or her birthweight is less than 2,500 grams. Construct a Venn diagram to illustrate the relationship between events A and B.
- For a randomly selected Mexican-American newborn, what is the probability that A or B or both occur?
- What is the probability that event A occurs given that event B occurs?
- Are A and B independent? Justify your answer mathematically.
- Following an industrial accident, lead concentrations in the air of a nearby factory were measured at multiple locations. The factory was divided into 1,000 equal spaces, and 100 measurements were used to estimate the mean and standard deviation. It was concluded that the lead concentrations followed an approximately normal distribution, and the sample mean levels of lead were 1.15μg/m3 with a sample standard deviation of 0.32 μg/m3. Note that the local environmental safety regulation states that levels above 1.50 μg/m3 are dangerous to health. Assuming a normal distribution and using the sample values for mean and standard deviation,
- What is the probability that concentrations exceed the safety limit imposed by regulations?
- We want to further study contaminated locations with lead concentrations that fell in the middle 70%. What lead concentrations did they have?
- Be able to calculate and correctly interpret probability data from a sampling distribution.
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Students mustViewReceive a gradeReceive a passing grade
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Answer key. Probability and Sampling Distributions File24.7 KB