Question

Scores on a statistics final in a large class were normally distributed with a mean of 76 and a standard deviation of 7. What is the probability that a randomly chosen student scored between 80 and 90?

If there are two answers, list both answers separated by a comma.

Answer 1

To find the probability that a student scored between 80 and 90 on the statistics final, calculate the z-scores for both scores and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a student scored between 80 and 90 on the statistics final, we need to calculate the z-scores for both scores and then use the standard normal distribution table. The z-score formula is: z = (x - mean) / standard deviation.

For a score of 80:
z = (80 - 76) / 7 = 4 / 7 ≈ 0.57

For a score of 90:
z = (90 - 76) / 7 = 14 / 7 = 2

Now we look up the probabilities associated with these z-scores. From the standard normal distribution table, the probability corresponding to a z-score of 0.57 is approximately 0.7131, and the probability corresponding to a z-score of 2 is approximately 0.9772.

Therefore, the probability that a randomly chosen student scored between 80 and 90 is approximately 0.9772 - 0.7131 = 0.2641.