Pregunta
The scores on a psychology exam were normally distributed with a
of 62 and a standard deviation of 8 . A failing grade on the exam wa
anything 2 or more standard deviations below the mean. What was
cutoff for a failing score? Approximately what percentage of the
students failed?
The cutoff for a failing score was 46 .
(Simplify your answer.)
Approximately
(Round to one decimal place as needed.)
of 62 and a standard deviation of 8 . A failing grade on the exam wa
anything 2 or more standard deviations below the mean. What was
cutoff for a failing score? Approximately what percentage of the
students failed?
The cutoff for a failing score was 46 .
(Simplify your answer.)
Approximately
(Round to one decimal place as needed.)
Ask by Beck Collins. in the United States
Jan 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The cutoff for a failing score is 46. Approximately 2.3% of the students failed.
Solución
To determine the cutoff for a failing score and the percentage of students who failed, let’s break down the problem step by step.
Given:
- Mean (μ) = 62
- Standard Deviation (σ) = 8
- Failing Grade = 2 or more standard deviations below the mean
1. Cutoff for a Failing Score:
The cutoff score is calculated as:
So, the cutoff for a failing score is 46.
2. Percentage of Students Who Failed:
We need to find the percentage of students scoring 46 or below. Since the scores are normally distributed, we can use the standard normal distribution (Z-score) to find this percentage.
Calculate the Z-score:
Find the corresponding percentile for
Using standard normal distribution tables or a calculator:
Rounding to one decimal place:
Final Answer:
Approximately 2.3 % of the students failed.
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Simplifique esta solución The Deep Dive
To find the cutoff for a failing score, you’ll subtract 2 standard deviations from the mean. Given a mean of 62 and a standard deviation of 8:
Cutoff = Mean - (2 × Standard Deviation) = 62 - (2 × 8) = 62 - 16 = 46.
Now, regarding the percentage of students who failed, you can refer to the properties of a normal distribution. About 95% of the scores should fall within two standard deviations of the mean, which means approximately 5% of students scored below 46, marking them as failing.
So, the percentage of students who failed is approximately 5.0%.
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