Quantitative SAT Scores, Normal and Binomial
The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed.
a. What is the probability that one randomly selected person will have an SAT score of 550 or more?
b. What is the probability that four randomly selected people will all have SAT scores of 550 or more?
c. For 800 randomly selected people, what is the probability that 250 or more will have scores of 550 or more?
d. For 800 randomly selected people, on average how many should have scores of 550 or more? Round to the nearest whole number.
e. Find the standard deviation for part d. Round to the nearest whole number.
f. Report the range of people out of 800 who should have scores of 550 or more from two standard deviations below the mean to two standard deviations above the mean. Use your rounded answers to part d and e.
g. If 400 out of 800 randomly selected people had scores of 550 or more, would you be surprised? Explain.