1. The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean μ = 296 and standard deviation σ = 39.
Choose one 12th-grader at random. What is the probability (±±0.1, that is round to one decimal place) that his or her score is higher than 296 ? ___ Higher than 374 (± 0.0001;____ that is round to 4 decimal places)?
Now choose an SRS of 16 twelfth-graders and calculate their mean score x? If you did this many times, what would be the mean of all the x-values?
What would be the standard deviation (±0.1; that is round to one decimal place) of all the x-values?
What is the probability that the mean score for your SRS is higher than 296?
than 296 ? (±0.1; that is round to 1 decimal place) Higher than 374 ? (±0.0001; that is round to 4 decimal places)
2. Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μof those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.4 . Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 26 .
If you choose one student at random, what is the probability (±0.0001; that is round to a 4th decimal place) that the student's score is between 20 and 30?
You sample 27 students. What is the standard deviation (±0.01, that is round to 2 decimal places) of sampling distribution of their average score x?
What is the probability (±0.0001; that is round to a 4th decimal place) that the mean score of your sample is between 20 and 30?