Question

3. [8 marks] Suppose a survey is conducted by Ipsos, a Canadian market research polling firm, on user satisfaction with cell phone coverage across the country. They sample 10 customers at random without replacement. Assume all sampled customers are independent. Suppose 30% of users nationwide are satisfied with their cell phone coverage. a) [5 marks] Calculate the probability that 3 or more of the 10 randomly sampled cell phone customers are satisfied with their cell phone coverage. b) [1 mark] Why is the probability that exactly 3 out of the 10 randomly sampled customers are satisfied with their cell phone coverage different from 0.3? Please answer in at most three sentences. c) [1 mark] On average, in a sample of 10 customers, how many do you expect to be satisfied with their cell phone coverage? d) [1 mark] Calculate the variance of the random variable associated with the number of satisfied customers.

Answer 1

3. Here p=0.30 which is same for all, n=10 is constant, events are independent and only two outcomes

Hence all the properties of binomial are satisfied

So we will use excel formula of binomial distribution to find required probabilities

a.

b.

c. Expected value is

d. Variance is