Assume your class took a final exam in psychology in which the scores produced a normal curve with a mean score of 80 and two standard deviations from the mean what is the possible range

General
1

Assume your class took a final exam in psychology in which the scores produced a normal curve with a mean score of 80 and two standard deviations from the mean what is the possible range

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Assume your class took a final exam in psychology in which the scores produced a normal curve with a mean score of 80 and two standard deviations from the mean, what is the possible range?

Answer:
To determine the possible range of scores that capture two standard deviations from the mean in a normal distribution, we need to understand a few key concepts about the normal curve or normal distribution:

  1. Mean (μ): This is the central point or average value in the normal distribution. For your psychology exam, the mean score is 80.

  2. Standard Deviation (σ): This measures the amount of variation or dispersion from the mean. Scores within one standard deviation from the mean fall within approximately 68% of all scores, within two standard deviations about 95%, and within three standard deviations about 99.7%.

Solution by Steps:

  1. Identify the Mean and Standard Deviation:

    • Given mean (μ): 80
    • Standard deviation (σ): Not directly given but let’s consider it a known value, say σ.

  2. Calculate the Range Within Two Standard Deviations:

    • Scores within two standard deviations from the mean cover approximately 95% of the data in a normal distribution.

    To capture two standard deviations from the mean, you would calculate as follows:

    • Lower range boundary: μ - 2σ
    • Upper range boundary: μ + 2σ

  3. Applying the Values:

    • Assuming we know the standard deviation is ( \sigma ):

      • Lower Boundary: ( 80 - 2\sigma )
      • Upper Boundary: ( 80 + 2\sigma )

    • Let’s assume (\sigma) is 10 (you will adjust this value based on the actual standard deviation if provided):

      • Lower Boundary: ( 80 - 2 \times 10 = 80 - 20 = 60 )
      • Upper Boundary: ( 80 + 2 \times 10 = 80 + 20 = 100 )

Final Answer:
Assuming a standard deviation of 10, the possible range of scores capturing two standard deviations from the mean is from 60 to 100. You should adjust this range based on the specific standard deviation value provided.

So, generally, the formula to find the range would be:
[ \text{Lower Range} = \mu - 2\sigma ]
[ \text{Upper Range} = \mu + 2\sigma ]

In Summary:
For a normal curve with mean 80 and extending two standard deviations from the mean, the possible range of scores is:
[ 80 \pm 2\sigma ]