I'm having trouble with these two questions:
1. Given average score = 70, standard deviation = 10, and assume scores follow normal distribution. 4 people are selected at random, what is probability that the AVERAGE of their scores is over 73 (i.e. 74 or above).
I'm having trouble with this average concept. It basically means that one person can get a failing mark let's say 49, but another person gets 100, then the average would be over 73. However the probability of getting a 69 or 71 aren't the same, as the central point (the mean) is at 70, not 50.
3. Second question is similar: given average score = 70, standard deviation = 10, if 300 students selected at random, what is probability that AT LEAST 175 students will have final score over 70?
Getting a score over 70 will have probability of 0.5 that I know, since mean = 70. But the numbers are way too large to calculate, since I gotta do (300 select 175)(0.5)^175(0.5)^125, and that's only if exactly 175 people get over score of 70. Gotta repeat that like 125 times. How do I approximate this using the binomial distribution curve? Isn't that curve used for approximating "approximately what % of people would get score x"?