Final answer:
The model for IQ scores is a Normal Model or Bell Curve, with the mean at 110 and standard deviation at 18. The central 95% of IQ scores are expected to fall within the interval of 74 to 146. About 17.7% of people are expected to have IQ scores above 92.
Step-by-step explanation:
To draw the model for the IQ scores, we use the Normal Model, also known as the Bell Curve. The mean is 110 and the standard deviation is 18. The 68-95-99.7 Rule states that approximately 68% of the scores will fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. Therefore, we can label the model with these percentages.
The central 95% of IQ scores would be found within 2 standard deviations of the mean. So, the interval for the central 95% of IQ scores would be from 110 - 2(18) to 110 + 2(18). This results in the interval from 74 to 146.
To determine the percent of people with IQ scores above 92, we need to find the area to the right of 92 on the model. This can be calculated using a z-table or calculator. The percentage is 1 minus the area to the left of 92, which is approximately 100% - 82.3% = 17.7%.
To find the percent of people with IQ scores between 74 and 92, we need to find the area between these two values on the model. This can also be calculated using a z-table or calculator. The percentage is the difference between the area to the left of 92 and the area to the left of 74, which is approximately 82.3% - 50% = 32.3%.
To find the percent of people with IQ scores below 56, we need to find the area to the left of 56 on the model. This can be calculated using a z-table or calculator, and is approximately 19.5%.