Questions: Look at this graph/illustration. This data illustrates how many people fall within the average when looking at how their performance in school matches their ability to succeed at future jobs. When looking at this data, Josh confidently declares that all of the people who "meet expectations" are 1 standard deviation from the mean while those rated as "below expectations" or "above expectations" are within 2 standard deviations from the mean. Josh is incorrect. There are several reasons why. Which choice correctly describes ONE of those reasons? The percentage of individuals within the first standard deviation must be 80% of the total data set. The percentage of individuals within the first standard deviation must be 75% of the total data set The percentage of individuals within the second standard deviation must be 95% of the total data set. The percentage of individuals within the second standard deviation must be 63% of the total data set.

Look at this graph/illustration. This data illustrates how many people fall within the average when looking at how their performance in school matches their ability to succeed at future jobs.

When looking at this data, Josh confidently declares that all of the people who "meet expectations" are 1 standard deviation from the mean while those rated as "below expectations" or "above expectations" are within 2 standard deviations from the mean. Josh is incorrect. There are several reasons why. Which choice correctly describes ONE of those reasons? The percentage of individuals within the first standard deviation must be 80% of the total data set. The percentage of individuals within the first standard deviation must be 75% of the total data set The percentage of individuals within the second standard deviation must be 95% of the total data set. The percentage of individuals within the second standard deviation must be 63% of the total data set.

Transcript text: Look at this graph/ilustration. This data ilustrates how many people fall within the average when looking at how their performance in school matches their ability to succeed at tuture jobs. When looking at this data, Josh confidently declares that all of the people who "meet expectations" are 1 staindard deviation from the mean while those rated as "below expectations" or "above expectations" are within 2 standard deviations from the mean. Josh is incorrect. There are several reasons why. Which choice correctly describes ONE of those reasons? The percentage of individuals within the first standard deviation must be $80 \%$ of the total data set. The percentage of indviduals within the first standard deviation must be $75 \%$ of the total data set The percentage of indviduals within the second standard deviation must be $95 \%$ of the total data set. The percentage of incliviuls within the second standard deviation must be $63 \%$ of the fotal data set.

Solution

Solution Steps

Step 1: Analyze the graph

The graph represents a normal distribution, often called a bell curve. The x-axis likely represents performance levels, while the y-axis represents the number of individuals at each performance level. The labels indicate the percentages of individuals falling into different performance categories. 50% meet expectations, 15% are below and above expectations, and 10% show minimum/unsatisfactory and excellent performances, respectively.

Step 2: Interpret Josh's statement

Josh claims that "meet expectations" is 1 standard deviation from the mean, and "below/above expectations" fall within 2 standard deviations. This implies he's interpreting the performance categories as standard deviation ranges.

Step 3: Evaluate Josh's statement against standard deviation rules

In a normal distribution:

Approximately 68% of data falls within 1 standard deviation of the mean.
Approximately 95% of data falls within 2 standard deviations of the mean.

Step 4: Identify the correct reason for Josh's error

Josh's interpretation doesn't align with the empirical rule (68-95-99.7 rule) for normal distributions. The graph shows 50% of people meeting expectations. This corresponds to the range within 1 standard deviation. Therefore, the first option is incorrect. It should be 68%, not 80%. The percentage of individuals within the second standard deviation also must be around 95%, not 75% as claimed by the second option. The fourth option is incorrect because 95% of individuals fall within 2 standard deviations in a normal distribution. Therefore, the third option correctly describes one reason why Josh is incorrect.