Answer :
The score that separates students who receive an F from those who do not is approximately 71.3.
To find the score that separates the lowest 4% of the class, we need to determine the cutoff point in terms of z-scores. A z-score measures how many standard deviations a value is from the mean in a normal distribution. We can use the standard normal distribution table or a statistical calculator to find the z-score corresponding to the lowest 4% of the distribution.
Since the teacher believes that the grades are normally distributed with a mean of 83 and a standard deviation of 5.5, we can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation. In this case, we want to find the z-score for the lowest 4%, which corresponds to an area of 0.04 under the normal curve.
Using a standard normal distribution table or calculator, we find that the z-score for an area of 0.04 is approximately -1.75.
Now we can solve for x in the z-score formula:
-1.75 = (x - 83) / 5.5
Simplifying the equation, we get:
-1.75 * 5.5 = x - 83
-9.625 = x - 83
x = 83 - 9.625
x ≈ 71.3
Therefore, the score that separates students who receive an F from those who do not is approximately 71.3.
Learn more about z-scores here:
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