Question

The average maximum monthly temperature in a city is 29.9 degrees Celsius. The standard deviation in maximum monthly temperature is 2.31 degrees. Assume that maximum monthly temperatures are normally distributed. Use this Rule of Thumb to complete the sentence. Round your answers to one decimal place. (Enter your answers from smallest to largest.) 95% of the time the maximum monthly temperature is between and degrees Celsius.

Answer 1

Answer: 95% of the time the maximum monthly temperature is between 25.28 degrees Celsius and 34.52 degrees Celsius.

Explanation:

The Range Rule of Thumb tells that the range is approximately four times the standard deviation.

95% of the data lies within 2 standard deviations from the mean .

Maximum usual value = Mean +2 (Standard deviation )

Minimum usual value = Mean - 2 (Standard deviation)

Given : Mean = 29.9 degrees Celsius

Standard deviation = 2.31 degrees Celsius

Then, according to the Range Rule of Thumb , we have

Maximum usual value = 29.9 +2 (2.31) = 34.52 degrees Celsius

Minimum usual value = 29.9 - 2 (2.31) = 25.28 degrees Celsius

i.e. 95% of the time the maximum monthly temperature is between 25.28 degrees Celsius and 34.52 degrees Celsius.