A random sample of 20 ages of world leaders yielded the following data: 54 66 53 49 50 65 82 62 65 63 47 76 68 71 72 78 77 88 72 59 a) Determine a 95% confidence interval for all the mean ages, , for all world leaders. Assume the population standard deviation is 11.2 years. (Note: the sum of the data is 1317.) b) Interpret your answer to part (a). 7) In a study, a sample of 26 students at a community college had a mean daily study time of 44.6 minutes. a) Assuming the study time of community college students is normally distributed with a standard deviation of 10.2 minutes, determine a 90% confidence interval for the mean daily study time of all community college students. b) Obtain the margin of error, E, for the confidence interval you found in (a). c) Explain the meaning of E in this context in terms of the accuracy of the estimate. d) Determine the sample size required to have a margin of error of 2.3 minutes with a 95% confidence interval.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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6) A random sample of 20 ages of world leaders yielded the following data:

54 66 53 49 50

65 82 62 65 63

47 76 68 71 72

78 77 88 72 59

a) Determine a 95% confidence interval for all the mean ages, , for all world leaders. Assume the population standard deviation is 11.2 years. (Note: the sum of the data is 1317.)
b) Interpret your answer to part (a).

7) In a study, a sample of 26 students at a community college had a mean daily study time of 44.6 minutes.

a) Assuming the study time of community college students is normally distributed with a standard deviation of 10.2 minutes, determine a 90% confidence interval for the mean daily study time of all community college students.
b) Obtain the margin of error, E, for the confidence interval you found in (a).
c) Explain the meaning of E in this context in terms of the accuracy of the estimate.
d) Determine the sample size required to have a margin of error of 2.3 minutes with a 95% confidence interval.

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.

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