Stress (Example 9) According to a 2017 Gallup poll, 80 % of Americans report being afflicted by stress. Suppose a random sample of 1000 Americans is selected. a. What percentage of the sample would we expect to report being afflicted by stress? b. Verify that the conditions for the Central Limit Theorem are met. c. What is the standard error for this sample proportion? d. According to the Empirical Rule , there is a 95 % probability that the sample proportion will fall between what two values?
Stress (Example 9) According to a 2017 Gallup poll, 80 % of Americans report being afflicted by stress. Suppose a random sample of 1000 Americans is selected. a. What percentage of the sample would we expect to report being afflicted by stress? b. Verify that the conditions for the Central Limit Theorem are met. c. What is the standard error for this sample proportion? d. According to the Empirical Rule , there is a 95 % probability that the sample proportion will fall between what two values?
Solution Summary: The author explains the central limit theorem by determining the percentage of Americans being affiliated by stress.
Stress (Example 9) According to a 2017 Gallup poll,
80
%
of Americans report being afflicted by stress. Suppose a random sample of 1000 Americans is selected.
a. What percentage of the sample would we expect to report being afflicted by stress?
b. Verify that the conditions for the Central Limit Theorem are met.
c. What is the standard error for this sample proportion?
d. According to the Empirical Rule, there is a
95
%
probability that the sample proportion will fall between what two values?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
Precalculus: Mathematics for Calculus (Standalone Book)
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