ECON1005: Introductory Statistics

Let x be a discrete random variable that possesses a binomial distribution

a Use the binomial formula to find the probability of P (x = 2) for n = 6 and p = .30

b Use Table 1 to verify your answer to part a). What do you notice?

c Calculate the mean and standard deviation of the probability distribution.

2. In an NPD Group survey of adults, 30% of 50-year-old or older (let us call them 50-plus) adult Americans said that they would be willing to pay more for healthier options at restaurants (USA TODAY, July 20, 2011). Suppose this result holds true for the current population of 50-plus adult Americans. A random sample of six 50-plus adult Americans is selected. Using Table I of Appendix C, answer the following.

(a) Find the probability that exactly three persons in this sample hold the said opinion.

(b) Find the probability that at most two persons in this sample hold the said opinion.

3 a) Obtain the following probabilities for the standard normal distribution.

i) P (z >-.98)

ii) P (-2.47 z 1.29)

b) Find the following area under a normal distribution curve with = 20 and = 4.

Area from x = 23 to x = 26

c) For a binomial probability distribution, n = 120 and p = .60. Let x be the number of successes in 120 trials. If the mean of the binomial distribution is 72 and the standard deviation is 5.367, find P (67 x 73) using the normal approximation.Note: Do not forget the continuity factor.