A local weather enthusiast wants to see if the last five summers have been warmer than normal for Eloy, Arizona. From the National Oceanic and Atmospheric Administration (NOAA), he knows the 30-year average for July was 90° with a standard deviation of 2. 1°. The last five summers recorded have an average of 93. 5°. If he uses a = 5%, which of the following would be valid based on the data he has gathered? He can conclude that the summers have been warmer than the 30-year average. He can conclude that the summers will continue to be warmer for the next 10 years. He does not have enough information to make a decision. The average for the last five years fits with the 30-year average.

For local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average.

The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The 30-year average for July was 90°. The standard deviation for this average is 2.1°. Thus, the temperature is lie between the ranges around the 90° in the month of July.

Therefore, the range of the temperature is,

The last five summers recorded have an average of 93. 5° and the value of a is 5%. Thus, the reduction is,

This value of temperature lies between the range of 87.9-92.1 degrees Celsius. Hence, the two average are probably the same.

Hence, for local weather of Eloy, Arizona, the average for the last five years fits with the 30-year average. Option D is correct.

Learn more about the standard deviation here;

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