1) Suppose the mean test scores for a college enter exam is normally distributed with mean = 78 and standard deviation = 12.
a). If an individual student is selected at random, what is the probability that this student's score is over 80?
b). A classroom of 16 of these students is used as a sample. What is the probability that the class mean is greater than 80?
2) A telemarketer makes a sale on 25% of his calls. If he makes 300 calls in a night, what is the probability that he will make more than 70 sales but less than 90 sales?
3) If 2% of the calls received by BMCC switchboard are wrong numbers. Find the probability that among 210 calls received by BMCC switchboard, 4 will be wrong numbers.
a). Determine in this case whether the conditions for the Poisson approximation to the Binomial distribution are satisfied.
b). If so, please use the Poisson approximation to the binomial distribution to find the probability.