a. Explanation Given info: The histogram shows the categorical distribution of hurricanes that have hit U.S. mainland. Based on the intensity of the hurricane, it is rated as 1 for the weakest and 5 for the strongest level. Calculation: From the histogram, the intensity level and its corresponding probabilities are identified. The probability distribution of hurricane hits is constructed below: Intensity level 1 2 3 4 5 Probability 0.418 0.261 0.247 0.063 0.010 The mean for the intensity level of hurricane hits is calculated as follows: Intensity level x Probability P ( x ) x ⋅ P ( x ) 1 0.418 0.418 2 0.261 0.522 3 0.247 0.741 4 0.063 0.252 5 0.01 0.05 Total 1 ∑ x ⋅ P ( x ) ≈ 2 Thus, the mean intensity level of hurricane hits is approximately 2. Variance: The variance for the probability distribution is calculated using the following formula: σ 2 = ∑ ( x − μ ) 2 P ( x ) Standard deviation: The standard deviation for the probability distribution is calculated using the formula: σ = σ 2 = ∑ ( x − μ ) 2 P ( x ) . The variance for the intensity level of hurricane hits is calculated as follows: Intensity level x Probability P ( x ) ( x − μ ) 2 ( x − μ ) 2 P ( x ) 1 0 b. To determine To give: The interpretation for the results obtained in part (a).

Elementary Statistics: Picturing the World (6th Edition)

6th Edition

ISBN: 9780321911216

Author: Ron Larson, Betsy Farber

Publisher: PEARSON

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Chapter 4.1, Problem 33E

To determine

To find: The mean, variance and standard deviation for the distribution of intensities of hurricane hits in the U.S. mainland.

To determine

To give: The interpretation for the results obtained in part (a).

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Chapter 4.1, Problem 32E

Chapter 4.1, Problem 34E

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Chapter 4 Solutions

Elementary Statistics: Picturing the World (6th Edition)

Ch. 4.1 - Prob. 1TY Ch. 4.1 - Prob. 2TY Ch. 4.1 - Prob. 3TY Ch. 4.1 - Prob. 4TY Ch. 4.1 - Prob. 5TY Ch. 4.1 - Prob. 6TY Ch. 4.1 - Prob. 7TY Ch. 4.1 - What is a random variable? Give an example of a...Ch. 4.1 - What is a discrete probability distribution? What...Ch. 4.1 - Is the expected value of the probability...

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The mean , variance and standard deviation for the distribution of intensities of hurricane hits in the U.S. mainland.

To find: The mean, variance and standard deviation for the distribution of intensities of hurricane hits in the U.S. mainland.

To give: The interpretation for the results obtained in part (a).

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Chapter 4 Solutions