1. If 62% of all clouds seeded with silver iodide show spectacular growth, what is the probability that among 24 clouds thus seeded exactly 15 will show spectacular growth? If the value given for this probability in the table of binomial probabilities is 0.1661, what is the error of the approximation?
2. A student answer each of the 48 questions on a multiple- choice test, each with four possible answers, by randomly drawing a card from an ordinary deck of 52 playing cards and checking first, second, third or fourth answer depending on whether the card drawn is a spade, heart, diamond, or club.
a) Use the normal curve approximation to find the probability that the student will get exactly 15 correct answers.
b) Use the normal curve approximation to find the probability that the student will get at least 15 correct answers.
3. The normal- curve approximation can also be used for discrete distribution other than the binomial distribution. For instance, it is reasonable to use this approximation if the Poisson distribution has parameter λ greater than 30. This approximation uses λ as the mean and as the standard deviation. Suppose that the number of false alarms received weekly by the fire department of a large city follows a Poisson distribution with λ = 45. In any given week, find the probability that
a) there will be 50 or more false alarms;
b) there will be at most 44 false alarms.