Question

the graph below shows the average daily temperatures on january 1 from 1900 to 1934 for city a.
average daily temperature
jan. 1 1900 - 1934
city a
the mean of the temperatures in the chart is 24° with a standard deviation of 4°. which temperature is within one standard deviation of the mean?

Explanation:

Step1: Determine the range for one standard deviation

The formula for the range within one standard deviation of the mean is \( \text{Mean} - \text{Standard Deviation} \) to \( \text{Mean} + \text{Standard Deviation} \). Given the mean (\( \mu \)) is \( 24^\circ \) and the standard deviation (\( \sigma \)) is \( 4^\circ \), we calculate the lower and upper bounds:
Lower bound: \( \mu - \sigma = 24 - 4 = 20^\circ \)
Upper bound: \( \mu + \sigma = 24 + 4 = 28^\circ \)

Step2: Identify temperatures within this range

We need to check which temperature lies between \( 20^\circ \) and \( 28^\circ \). (Assuming typical temperatures from the graph, e.g., if temperatures are 18, 22, 26, 30, etc., 22, 26 are within 20 - 28. Let's say a temperature like \( 22^\circ \) or \( 26^\circ \) is given. For example, if the options include 22, 26, etc., they are within the range. Let's take a specific example: if a temperature is \( 26^\circ \), check if \( 20 \leq 26 \leq 28 \), which is true. So any temperature between 20 and 28 (inclusive) is within one standard deviation.

Answer:

A temperature between \( 20^\circ \) and \( 28^\circ \) (e.g., \( 22^\circ \), \( 26^\circ \), etc., depending on the options. If a specific temperature like 26 is an option, then 26 is within the range as \( 20 \leq 26 \leq 28 \)).