Grade point averages of students on a large campus follow a normal distribution with a mean of 2.6 and a standard deviation of 0.5.a. One student is chosen at random from this campus. What is the probability that this student has a grade point average higher than 3.0?b. One student is chosen at random from this campus. What is the probability that this student has a grade point average between 2.25 and 2.75?c. What is the minimum grade point average needed for a student’s grade point average to be among the highest 10% on this campus?d. A random sample of 400 students is chosen from this campus. What is the probability that at least 80 of these students have grade point averages higher than 3.0?e. Two students are chosen at random from this campus. What is the probability that at least one of them has a grade point average higher than 3.0?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Grade point averages of students on a large campus follow a
a. One student is chosen at random from this campus. What is the
b. One student is chosen at random from this campus. What is the probability that this student has a grade point average between 2.25 and 2.75?
c. What is the minimum grade point average needed for a student’s grade point average to be among the highest 10% on this campus?
d. A random sample of 400 students is chosen from this campus. What is the probability that at least 80 of these students have grade point averages higher than 3.0?
e. Two students are chosen at random from this campus. What is the probability that at least one of them has a grade point average higher than 3.0?
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