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------------------------------------------------ A set of grades on a math exam is normally distributed with a mean of 70 and a standard deviation of 16.9. If the lowest 20% of the students are given an F, then the lowest passing grade is approximately equal to:

A. 50
B. 56
C. 70
D. 69

To find the lowest passing grade out of 300 questions, we need to determine the score that corresponds to the lowest 20% of the students. Since the grades on the math exam are normally distributed with a mean of 70 and a standard deviation of 16.9, we can use the properties of a normal distribution to solve this problem.

First, we need to find the z-score corresponding to the lowest 20% of the students. The z-score represents the number of standard deviations a data point is from the mean. We can use a standard normal distribution table or a calculator to find the z-score.

From the standard normal distribution table, we find that the z-score corresponding to the lowest 20% is approximately -0.84.

Next, we can use the formula for z-score to find the corresponding raw score:

z = (x - mean) / standard deviation

Substituting the values, we have:

-0.84 = (x - 70) / 16.9

Solving for x, we get:

x - 70 = -0.84 * 16.9

x - 70 = -14.196

x = 70 - 14.196

x ≈ 55.804

Therefore, the lowest passing grade out of 300 questions is approximately 55.804.

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