Use the normal distribution of SAT critical reading scores for which the mean is 505 and the standard deviation is 114. Assume the variable $x$ is normally distributed. (a) What percent of the SAT verbal scores are less than 675 ? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550 ? Click to view page 1 of the standard normal table. Click to view page 2 of the standard normal table. (a) Approximately $93.20 \%$ of the SAT verbal scores are less than 675 (Round to two decimal places as needed.) (b) You would expect that approximately SAT verbal scores would be greater than 550 . (Round to the nearest whole number as needed.)

Step 1 ：Given that the mean (\(\mu\)) is 505 and the standard deviation (\(\sigma\)) is 114, we want to find the percentage of SAT verbal scores less than 675 and the expected number of scores greater than 550 out of 1000.

Step 2 ：For part (a), we first calculate the z-score for 675. The z-score is calculated as \(z = \frac{x - \mu}{\sigma}\). Substituting the given values, we get \(z_a = \frac{675 - 505}{114} = 1.4912280701754386\).

Step 3 ：We then look up this z-score in the standard normal table to find the corresponding percentile. The percentile for \(z_a = 1.4912280701754386\) is approximately 93.20\%.

Step 4 ：\(\boxed{\text{Therefore, approximately 93.20\% of the SAT verbal scores are less than 675.}}\)

Step 5 ：For part (b), we calculate the z-score for 550 in the same way as in part (a). We get \(z_b = \frac{550 - 505}{114} = 0.39473684210526316\).

Step 6 ：We look up this z-score in the standard normal table to find the corresponding percentile. The percentile for \(z_b = 0.39473684210526316\) is approximately 65.35\%.

Step 7 ：This means that approximately 65.35\% of the scores are less than 550. To find the proportion of scores that are greater than 550, we subtract this value from 1. We get \(1 - 0.6535 = 0.3465\).

Step 8 ：To find the expected number of scores greater than 550 out of 1000, we multiply this proportion by 1000. We get \(0.3465 \times 1000 = 346.51855503363174\).

Step 9 ：\(\boxed{\text{Therefore, we would expect that approximately 347 SAT verbal scores would be greater than 550.}}\)