Question

In: Statistics and Probability

Seventy percent of all individuals living in the United States have a smart phone. Suppose you...

Seventy percent of all individuals living in the United States have a smart phone. Suppose you select a random sample of 11 individuals who live in the United States. Define X to be a binomial random variable representing whether or not an individual living in the United States has a smart phone.

What is the probability that no more than five of the sampled individuals have a smart phone? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 3 decimal places, using conventional rounding rules)

What is the probability that at least 7, but less than 11, of the sampled individuals have a smart phone? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 3 decimal places, using conventional rounding rules)

On average, how many of the eleven sampled individuals would you expect to have a smart phone? ANSWER: (Report your answer to 3 decimal places, using conventional rounding rules)

Solutions

Expert Solution

p = 0.7

n = 11

P(X = x) = 11Cx * 0.7x * (1 - 0.7)11-x

a) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

                  = 11C0 * 0.70 * 0.311 + 11C1 * 0.71 * 0.310 + 11C2 * 0.72 * 0.39 + 11C3 * 0.73 * 0.38 + 11C4 * 0.74 * 0.37 + 11C5 * 0.75 * 0.36

                  = 0.078

b) P(7 < x < 11) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

                          = 11C7 * 0.77 * 0.34 + 11C8 * 0.78 * 0.33 + 11C9 * 0.79 * 0.32 + 11C10 * 0.710 * 0.31

                          = 0.770

c) Expected value = n * p = 11 * 0.7 = 7.7


Related Solutions

Seventy percent of all individuals living in the United States have a smart phone. Suppose you...
Seventy percent of all individuals living in the United States have a smart phone. Suppose you select a random sample of 11 individuals who live in the United States. Define X to be a binomial random variable representing whether or not an individual living in the United States has a smart phone. a.) What is the probability that no more than five of the sampled individuals have a smart phone? b.) What is the probability that at least 7, but...
(a). Now the population is all senior living facilities in the United States. It is conjectured...
(a). Now the population is all senior living facilities in the United States. It is conjectured that the mean number of positive COVID-19 cases per 100 residents is 40, and of interest is to test this conjecture versus the alternative that the mean number of positive COVID-19 cases per 100 residents is different from 40. State the appropriate null and alternative hypotheses that should be tested. (b). Consider the information and hypotheses specified in part (a). A simple random sample...
Phone Corporation owns 80 percent of Smart Company's stock. At the end of 20X8, Phone and...
Phone Corporation owns 80 percent of Smart Company's stock. At the end of 20X8, Phone and Smart reported the following partial operating results and inventory balances: Phone Corporation Smart Company Total sales $ 679,000 $ 519,000 Sales to Smart Company 150,500 Sales to Phone Corporation 250,500 Net income 31,000 Operating income (excluding investment income from Smart) 81,000 Inventory on hand, December 31, 20X8, purchased from: Smart Company 50,100 Phone Corporation 45,150 Phone regularly prices its products at cost plus a...
Consider the sample space of all people living in the United States, and within that sample...
Consider the sample space of all people living in the United States, and within that sample space, the following two events. ??=people who are college graduates=people who are unemployedA=people who are college graduatesB=people who are unemployed Suppose the following statements describe probabilities regarding these two events. Which of the statements describe conditional probabilities? Select all that apply. The probability is 4.1% that a college graduate is unemployed. Twenty‑six point two percent of unemployed people are college graduates. There is a...
Suppose that the annual interest rate is 5.0 percent in the United States and 3.5 percent...
Suppose that the annual interest rate is 5.0 percent in the United States and 3.5 percent in Germany, and that the spot exchange rate is $1.12/€ and the forward exchange rate, with oneyear maturity, is $1.16/€. Assume that an arbitrager can borrow up to $1,000,000 or € 892,857.14 a) Show how to realize a certain profit via covered interest arbitrage. b) Using given spot rate answer what is the one-year forward rate that should prevail if rates of inflation expected...
Suppose that the annual interest rate is 3 percent in the United States and 4 percent...
Suppose that the annual interest rate is 3 percent in the United States and 4 percent in Germany, and that the S(EUR/USD) = $1.60 and the forward exchange rate, with one-year maturity, is F12(EUR/USD ) = $1.57. Assume that an arbitrager can borrow up to $10,000,000 or €6,250,000. If an astute trader finds an arbitrage opportunity, what is the net cash flow in one year? (Show each step and the values)
Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Suppose...
Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Suppose a random sample of 12 cars is selected. Assuming that successive vehicles pass or fail independently of one another calculate each of the following. a.)What is the expected number of vehicles to pass? b.)What is the probability that the number of the 12 cars selected that pass is within one standard deviation of the expected value?
1.) You are living in the United States and are thinking of traveling to Germany 6...
1.) You are living in the United States and are thinking of traveling to Germany 6 months from now. You can purchase an option to buy euros now at a fixed rate of $1.50 per euro 6 months from now. How is the option like an insurance policy? 3.) You buy stock worth $50. In one year, it pays a dividend of $5 and is worth $60 right after the dividend is paid. What are the dividend income component, price...
Suppose that the inflation rate in the United States is 1.5 percent while GDP is 2...
Suppose that the inflation rate in the United States is 1.5 percent while GDP is 2 percent below the potential level. According to the Taylor Rule the Federal Reserve authorities should adjust the stock of base money to drive the target inflation rate to 2 percent. If the current federal funds rate is 2.75 percent, does this mean that the U.S. monetary policy is too tight? Explain (assume the real natural rate of interest is 2 percent and α =...
2. Suppose that the annual interest rate is 2.0 percent in the United States and 4...
2. Suppose that the annual interest rate is 2.0 percent in the United States and 4 percent in Germany, and that the spot exchange rate is $1.60/€ and the forward exchange rate, with one-year maturity, is $1.58/€. Assume that an arbitrager can borrow up to $1,000,000 or €625,000 a. Determine whether the interest rate parity is currently holding. b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT