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[39] The mean of the daily high temperatures for a 5-day period in a certain city was recorded as being 4.0°F. It was later determined that the high temperature for 1 of these 5 days was recorded incorrectly. If that day's high temperature was 2°F higher than originally recorded, what is the difference between the incorrectly recorded mean and the correct mean?

Question

[39] The mean of the daily high temperatures for a 5-day period in a certain city was recorded as being 4.0°F. It was later determined that the high temperature for 1 of these 5 days was recorded incorrectly. If that day's high temperature was 2°F higher than originally recorded, what is the difference between the incorrectly recorded mean and the correct mean?

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Solution

The problem can be solved in the following steps:

Step 1: Find the total sum of the temperatures for the 5-day period. Since the mean was 4.0°F, the total sum would be 4.0°F * 5 = 20.0°F.

Step 2: Correct the error in the recorded temperature. The problem states that one day's temperature was 2°F higher than originally recorded. So, the correct total sum of temperatures would be 20.0°F + 2.0°F = 22.0°F.

Step 3: Find the correct mean temperature. The mean is the total sum divided by the number of days. So, the correct mean would be 22.0°F / 5 = 4.4°F.

Step 4: Find the difference between the incorrectly recorded mean and the correct mean. The difference would be 4.4°F - 4.0°F = 0.4°F.

So, the difference between the incorrectly recorded mean and the correct mean is 0.4°F.

This problem has been solved

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