# What is the probability that a single student randomly chosen from all those taking the test scores?

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with a mean 542.5 and a standard deviation of 29.7. (a) What is the probability that a single student randomly chosen from all those taking the test scores 547 or higher? Probability = (Expressing the probability as a proportion and rounding it to 4 decimal places) For parts (b) through (c), consider a random sample of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score X¯X¯, of 30 students? The mean of the sampling distribution for X¯X¯is: The standard deviation of the sampling distribution for X¯X¯is: (Rounding the standard deviation to 6 decimal places ) (c) What is the probability that the mean score X¯X¯of these students is 547 or higher? Probability = (Expressing the probability as a proportion and rounding it to 4 decimal places)