The mean IQ score for 1500 students is 95 , with a standard deviation of 15 . Assuming the scores have a normal curve, answer the following. a. How many have an IQ score between 80 and 110 ? b. How many have an IQ score between 65 and 125 ? c. How many have an IQ score over 140 ? a. The number of students with an IQ score between 80 and 110 is (Round to the nearest person as needed.)

To calculate the number of students with an IQ score between 80 and 110, we first need to determine how many standard deviations 80 and 110 are from the mean. The mean is 95, and the standard deviation is 15. - For 80: \( z = \frac{80 - 95}{15} = -1.00 \) - For 110: \( z = \frac{110 - 95}{15} = 1.00 \) Using the z-score table, the area under the curve for \( z = -1.00 \) is about 0.1587, and for \( z = 1.00 \), it is around 0.8413. Thus, the area between these two z-scores is: \( 0.8413 - 0.1587 = 0.6826 \) Now, we multiply this area by the total number of students: \( 0.6826 \times 1500 \approx 1024 \) So, approximately **1024 students** have an IQ score between 80 and 110. --- How about using z-scores to make life easier? Z-scores let you standardize your data, making it straightforward to determine how many students fall within specific ranges. Just remember, a z-score represents how many standard deviations an element is from the mean. It’s a nifty trick to quickly analyze scores without getting overwhelmed by raw data! Also, keep an eye on the tails of the normal distribution! Scores over 140 fall into the upper tail, where the math gets a bit spicy. Calculating for scores above 140 would use \( z = \frac{140 - 95}{15} \), leading us to find the area under that curve’s tail, giving us a glimpse into the genius levels among your students!