(a) If a student is randomly selected, find the probability that the verbal score is above 500. (b) If 75 students who took the SAT are selected at random, find the probability that their mean verbal score is above 500. (c) If a sample of 15 students is selected randomly, would it be appropriate to use the same methods as in (b) to find the probability that the sample mean is above 500? Why or why not?

MATLAB: An Introduction with Applications
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For questions (a) and (b):

1) Write the probability statement

2) Draw and label a sketch of the distribution, indicating what it is that you are looking for, etc.

3) Show all work

4) Round to 4 decimal places, a and circle your answer

Then, answer (c).

SAT verbal scores are approximately normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP).

(a) If a student is randomly selected, find the probability that the verbal score is above 500.

(b) If 75 students who took the SAT are selected at random, find the probability that their mean verbal score is above 500.

(c) If a sample of 15 students is selected randomly, would it be appropriate to use the same methods as in (b) to find the probability that the sample mean is above 500? Why or why not?

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