Question

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 92°. If he uses a = 2.5%, which of the following would be valid based on the data he has gathered?


A) He can conclude that the summers have been warmer than the 30-year average.
B) He can conclude that the summers will continue to be warmer for the next 10 years.
C) He does not have enough information to make a decision.
D) The average for the last five years fits with the 30-year average.

Answer 1

The correct answer to which is the valid conclusion based on the date gathered by the local weather enthusiast is D. The average for the last five years fits with the 30-year average. Based on the given facts, the average of five summer recorded is 92 degrees. There is a standard deviation of 2.1 degrees which makes it fir to the 30-year plan.

Answer 2

Answer with Explanation:

Average in Temperature in last 30 years in the month of July for Eloy and Arizona=90°

Standard Deviation =2.1°

→It means ,temperature of last 30 years of states Eloy and Arizona lie between , 90°-2.1° to 90°+2.1°= 87.9° to 90°.

→→Average of last five Summers, for Eloy and Arizona=92°

a=2.5%

Calculating , the reduction ,which is equal to 2.5% from 92

 $=92-92\times \frac{2.5}{100}\\\\=92 -2.30\\\\=89.70$

→89.70° lies between ,87.9° to 90°.

So,we can confidently assert  that→the two averages are probably same.

Option D: The average for the last five years fits with the 30-year average.