Question

The probability that a randomly selected medical student who took the test had a total score between 497 and 510 is:

A. Calculate the mean and standard deviation of the test scores.
B. Use the normal distribution to find the z-scores.
C. Apply the z-table to determine probabilities.
D. Interpret the results in the context of the test scores.

Answer 1

To calculate the probability of a specific range of test scores, you need to know the mean and standard deviation, calculate the z-scores, use the z-table to find the probabilities, and interpret the results.

Correct option is A

Step-by-step explanation:

To calculate the probability that a randomly selected medical student who took the test had a total score between 497 and 510, we need to use the normal distribution and z-scores. Here are the steps:

1. Calculate the mean and standard deviation of the test scores. The mean is the average score and the standard deviation measures the spread of the scores.
2. Use the z-score formula to find the z-scores for the lower and upper bounds of the desired range. The z-score formula is z = (x - mean) / standard deviation.
3. Look up the probabilities corresponding to the z-scores in the z-table. The z-table provides the areas under the normal curve.
4. Calculate the probability of the desired range by subtracting the lower z-score probability from the upper z-score probability.
5. Interpret the results by explaining what the probability represents in the context of the test scores.