Questions: This question: 3 point(s) possible The ages (years) of three government officials when they died in office were 56, 46, and 60. Complete parts (a) through (d). a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples. A. (56,56),(56,46),(56,60),(46,46),(46,60),(60,60) B. (56,56),(56,46),(56,60),(46,56),(46,46),(46,60),(60,56),(60,46),(60,60) C. (56,46),(56,60),(46,60) D. (56,46),(56,60),(46,56),(46,60),(60,56),(60,46) b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability

This question: 3 point(s) possible The ages (years) of three government officials when they died in office were 56, 46, and 60. Complete parts (a) through (d). a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples. A. (56,56),(56,46),(56,60),(46,46),(46,60),(60,60) B. (56,56),(56,46),(56,60),(46,56),(46,46),(46,60),(60,56),(60,46),(60,60) C. (56,46),(56,60),(46,60) D. (56,46),(56,60),(46,56),(46,60),(60,56),(60,46) b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability
Transcript text: This question: 3 point(s) possible The ages (years) of three government officials when they died in office were 56, 46, and 60. Complete parts (a) through (d). a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples. A. $(56,56),(56,46),(56,60),(46,46),(46,60),(60,60)$ B. $(56,56),(56,46),(56,60),(46,56),(46,46),(46,60),(60,56),(60,46),(60,60)$ C. $(56,46),(56,60),(46,60)$ D. $(56,46),(56,60),(46,56),(46,60),(60,56),(60,46)$ b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability
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Solution

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Solution Steps

Step 1: List all possible samples

For a population of 3 individuals, with ages [56, 46, 60], there are 9 possible samples. Samples: [(56, 56), (56, 46), (56, 60), (46, 56), (46, 46), (46, 60), (60, 56), (60, 46), (60, 60)]

Step 2: Calculate the range for each sample

Sample ranges: [0, 10, 4, 10, 0, 14, 4, 14, 0]

Step 3: Summarize the sampling distribution of the ranges

Sample Range | Probability 0 | 0.33 4 | 0.22 10 | 0.22 14 | 0.22

Step 4: Compare the population range to the mean of the sample ranges

Population range: 14 Mean of sample ranges: 6.22

Final Answer:

The population range is 14, while the mean of the sample ranges is 6.22.

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