Suppose X is a geometric random variable with probability of success p 5 0.40 and Y is a binomial random variable with the same probability of success p 5 0.40. For a 5 1, 2, 3, c, 10, construct a table with the following probabilities.
Carefully examine the table and write a general formula to explain each equality. Can you prove these results?
Emergency defibrillators are now located in many public buildings. However, the U.S. Food and Drug Administration (FDA) is concerned about the reliability of these devices. Approximately 45,000 devices failed during the past seven years.41 Suppose the FDA claims that the probability of an emergency defibrillator working correctly is 0.90, and 30 of these devices are selected at random and tested.
a. Find the probability that exactly 28 devices will work correctly.
b. Find the probability that at least 25 devices will work correctly.
c. Suppose only 20 of the devices work correctly. Is there any evidence to suggest that the proportion of emergency defibrillators that work correctly has changed? Justify your answer.
IKEA is a Swedish company that sells ready-to-assemble furniture. Shoppers contact customer service with regard to finding a nearby store, online shipping questions, and even for help with assembly. IKEA classifies all telephone calls to its customer support staff by the amount of time the customer is on hold. If the customer is on hold for no more than 60 seconds, then the call is classified as successful (actually, this sounds like a miracle). The supervisor in technical support claims 80% of all calls are successful. Suppose 25 calls to technical support are selected at random.
a. Find the mean, variance, and standard deviation of the number of successful calls.
b. Find the probability that at least 18 calls will be successful.
c. Suppose 21 calls are successful. Is there any evidence to suggest the supervisor’s claim is false? Justify your answer.