Use the table to answer the question.

The mean score on a quiz is 80, with a standard deviation of 8. What is the probability that a randomly selected student scored below 73 on the quiz?

(1 point)
The probability that a randomly selected student scored below 73 is %

1 answer

To find the probability that a randomly selected student scored below 73 on the quiz, you can use the properties of the normal distribution, as the distribution of scores is typically assumed to be normal.

Given:

  • Mean (\(\mu\)) = 80
  • Standard deviation (\(\sigma\)) = 8

First, you need to calculate the z-score for the score of 73 using the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

Where:

  • \(X\) is the score you are comparing (73 in this case),
  • \(\mu\) is the mean (80),
  • \(\sigma\) is the standard deviation (8).

Substituting the values:

\[ z = \frac{(73 - 80)}{8} = \frac{-7}{8} = -0.875 \]

Next, you can look up the z-score of -0.875 in a standard normal distribution table, or use a calculator or statistical software to find the corresponding probability.

The probability associated with a z-score of -0.875 is approximately 0.1915.

Thus, the probability that a randomly selected student scored below 73 is about 0.1915, or 19.15%.

Therefore, the probability that a randomly selected student scored below 73 is approximately 19.15%.