Question

300 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and a standard deviation of 4. How many students scored between 16 and 32 ?

Answer 1

To find the number of students who scored between 16 and 32 on the ACT, we calculate the z-scores for those scores and use the z-table to find the corresponding probabilities. Approximately 95.44% of the students scored between 16 and 32 on the ACT.

Step-by-step explanation:

To find the number of students who scored between 16 and 32 on the ACT, we need to calculate the z-scores for those scores and then use the z-table to find the corresponding probabilities.

First, let's find the z-score for 16:

z = (x - mean) / standard deviation

z = (16 - 24) / 4 = -2

Now let's find the z-score for 32:

z = (32 - 24) / 4 = 2

Using the z-table, we can find the probabilities associated with these z-scores. The area to the left of -2 is 0.0228 and the area to the left of 2 is 0.9772. To find the area between -2 and 2, we subtract the smaller area from the larger area:

0.9772 - 0.0228 = 0.9544

Therefore, approximately 95.44% of the students scored between 16 and 32 on the ACT.