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The data set represents the income levels of the members of a country club. Use the relative frequency method to estimate the probability that a randomly selected member earns at least $83,000.

Data Set:
- 89,000
- 83,012
- 81,000
- 83,015
- 82,000
- 83,006
- 83,000
- 82,996
- 83,021
- 83,036
- 83,018
- 82,000
- 83,012
- 83,009
- 83,000
- 83,024
- 82,995
- 83,009
- 82,997
- 83,003

Answer :

The probability that a randomly selected member of the country club earns at least $83,000 is 55%.

To estimate the probability that a randomly selected member earns at least $83,000, we first need to count how many members earn $83,000 or more and then divide that number by the total number of members.

Counts:
Number of members earning $83,000 or more: 11 (all incomes $83,000 and above are counted)
Total number of members: 20

Probability calculation:
The probability (P) that a randomly selected member earns at least $83,000 is P = (Number of members earning $83,000 or more) / (Total number of members) = 11 / 20 = 0.55 or 55%.

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Rewritten by : Barada

Using the relative frequency method, we can estimate the probability of a randomly selected member from a country club earning at least $83,000.

The given dataset provides the income levels of club members. We will calculate the relative frequency of incomes equal to or greater than $83,000 to estimate the desired probability.

To estimate the probability, we need to calculate the relative frequency of incomes equal to or greater than $83,000. The dataset provided includes the following income levels: 89,000; 83,012; 81,000; 83,015; 82,000; 83,006; 83,000; 82,996; 83,021; 83,036; 83,018; 82,000; 83,012; 83,009; 83,000; 83,024; 82,995; 83,009; 82,997; and 83,003.

First, we count the number of incomes that are equal to or greater than $83,000. In this case, we have 10 incomes that meet this criterion.

Next, we calculate the relative frequency by dividing the count of incomes equal to or greater than $83,000 by the total number of incomes in the dataset. Since the dataset contains 20 income levels, the relative frequency is 10/20 = 0.5.

Therefore, using the relative frequency method, we estimate that the probability of randomly selecting a member from the country club who earns at least $83,000 is approximately 0.5 or 50%.

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