Brainly AI Helper:
1. To find the probability that a student scores less than 450 on the SAT math test, we need to first calculate the z-score for this score. The z-score formula is: z = (X - μ) / σ, where X is the value we are interested in (450 in this case), μ is the mean (511), and σ is the standard deviation (110).
2. Plugging in the values, we get: z = (450 - 511) / 110 = -0.5545. This means that a score of 450 is 0.5545 standard deviations below the mean.
3. Now, we need to look up the corresponding area under the standard normal curve for a z-score of -0.5545. By using a standard normal distribution table or a calculator, we find that the area to the left of z = -0.5545 is approximately 0.2903.
4. Therefore, the probability that a student chosen at random will score less than 450 on the SAT math test is 0.2903, or approximately 29.03%. This represents the shaded area under the normal curve to the left of the z-score corresponding to a score of 450.
