QuestionJune 26, 2025

A teacher informs his macro economics class (of 500+students) that a test was very difficult, but the grades would be curved . Scores on the test were normally distributed with a mean of 44.2 and a standard deviation of 9.4. Round your answers to at least one decimal place. (a) If the top 14% will receive an A,what is the minimum score to get an A? square (b) If the bottom 33% will receive an F, what is the minimum score to pass the class? square

A teacher informs his macro economics class (of 500+students) that a test was very difficult, but the grades would be curved . Scores on the test were normally distributed with a mean of 44.2 and a standard deviation of 9.4. Round your answers to at least one decimal place. (a) If the top 14% will receive an A,what is the minimum score to get an A? square (b) If the bottom 33% will receive an F, what is the minimum score to pass the class? square
A teacher informs his macro economics class (of 500+students) that a test was very difficult, but the grades would be curved . Scores on the test were normally distributed with a mean of 44.2 and a standard deviation of 9.4. Round your answers to at least one decimal place. (a) If the top 14% will receive an A,what is the minimum score to get an A? square (b) If the bottom 33% will receive an F, what is the minimum score to pass the class? square

Solution
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Answer

(a) Minimum score to get an A: 54.4 ### (b) Minimum score to pass the class: 40.0 Explanation 1. Find the Z-score for top 14% Use the standard normal distribution table to find the Z-score corresponding to the top 14%. The Z-score is approximately 1.08. 2. Calculate minimum score for an A Use the formula: X = \mu + Z \cdot \sigma. Here, \mu = 44.2, \sigma = 9.4, and Z = 1.08. Calculate X = 44.2 + 1.08 \cdot 9.4. 3. Find the Z-score for bottom 33% Use the standard normal distribution table to find the Z-score corresponding to the bottom 33%. The Z-score is approximately -0.44. 4. Calculate minimum score to pass Use the formula: X = \mu + Z \cdot \sigma. Here, \mu = 44.2, \sigma = 9.4, and Z = -0.44. Calculate X = 44.2 - 0.44 \cdot 9.4.

Explanation

1. Find the Z-score for top 14%<br /> Use the standard normal distribution table to find the Z-score corresponding to the top 14%. The Z-score is approximately $1.08$.<br /><br />2. Calculate minimum score for an A<br /> Use the formula: $X = \mu + Z \cdot \sigma$. Here, $\mu = 44.2$, $\sigma = 9.4$, and $Z = 1.08$. Calculate $X = 44.2 + 1.08 \cdot 9.4$.<br /><br />3. Find the Z-score for bottom 33%<br /> Use the standard normal distribution table to find the Z-score corresponding to the bottom 33%. The Z-score is approximately $-0.44$.<br /><br />4. Calculate minimum score to pass<br /> Use the formula: $X = \mu + Z \cdot \sigma$. Here, $\mu = 44.2$, $\sigma = 9.4$, and $Z = -0.44$. Calculate $X = 44.2 - 0.44 \cdot 9.4$.
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