Can you help me with problem 5.16

5.2 Binomial Distribution 187 FIGURE 5.6 A B C D E In the Worksheet Excel results for 1 Probability of Correct Order at Wendy's computing the The worksheet uses short arithmetic Data binomial probability Sample size formulas to compute parameters and the Probability of an event of interest 0.391 for Example 5.4 probabilities in columns D through F. Parameters The worksheet uses the BINOM.DIST Mean function to compute probabilities in 9 Variance 0.3914 10 Standard deviation 0.5198 columns B and C. 11 12 Binomial Probabilities Table The CUMULATIVE worksheet of the 13 14 0.0613 6.0013 6.0000 0.5987 1-6060 Excel Guide Binomial workbook is a 15 1 0.0318 0.0831 0.0013 0.9469 0.9987 copy of the Figure 5.6 worksheet. 2 0.2596 0 7927 1 0.7073 1.0000 0.2927 0,0000 0.7073 PROBLEMS FOR SECTION 5.2 LEARNING THE BASICS 5.14 A manufacturing company regularly conducts quality con- 5.9 Determine the following: trol checks at specified periods on the products it manufactures. a. For n = 4 and 7 = 0.12, what is P(X = 0)? Historically, the failure rate for LED light bulbs that the company b. For n = 10 and #7 = 0.40, what is P(X = 9)? manufactures is 3%. Suppose a random sample of 10 LED light C. For n = 10 and #7 = 0.50, what is P(X = 8)? bulbs is selected. What is the probability that d. For n = 6 and # = 0.83, what is P(X = 5)? a. none of the LED light bulbs are defective? b. exactly one of the LED light bulbs is defective? 5.10 Determine the mean and standard deviation of the variable X c. two or fewer of the LED light bulbs are defective? in each of the following binomial distributions: d. three or more of the LED light bulbs are defective? a. n = 4 and 7 = 0.10 b. n = 4 and 7 = 0.40 5.15 Past records indicate that the probability of online retail orders that C. n = 5 and 7 = 0.80 turn out to be fraudulent is 0.08. Suppose that, on a given day, 20 online d. n = 3 and 7 = 0.50 retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable. APPLYING THE CONCEPTS a. What are the mean and standard deviation of the number of on- line retail orders that turn out to be fraudulent? 5.11 The increase or decrease in the price of a stock between the b. What is the probability that zero online retail orders will turn beginning and the end of a trading day is assumed to be an equally out to be fraudulent? likely random event. What is the probability that a stock will show c. What is the probability that one online retail order will turn out an increase in its closing price on five consecutive days? to be fraudulent? 5.12 In the last quarter of 2018, 47% of U.S. smartphone owners d. What is the probability that two or more online retail orders will turn out to be fraudulent? owned an iPhone. Source: Data extracted from pewrsuch/2riDGV6. SELF 5.16 In Example 5.4 that begins on page 186, you and TEST Using the binomial distribution, what is the probability that of the two friends decided to go to Wendy's. Now, suppose that instead you go to Burger King, which recently filled approximately next six Americans who own a smartphone surveyed, 90.9% of orders correctly. What is the probability that a. four will own an iPhone? a. all three orders will be filled correctly? b. all six will own an iPhone? b. none of the three will be filled correctly? c. at least four will own an iPhone? c. at least two of the three will be filled correctly? d. What are the mean and standard deviation of the number of American d. What are the mean and standard deviation of the binomial dis- smartphone owners who own an iPhone in a survey of six? tribution used in (a) through (c)? Interpret these values. e. What assumptions do you need to make in (a) through (c)? e. Compare the results of (a) through (d) with those of Wendy's in 5.13 A student is taking a multiple-choice exam in which each Example 5.4 and Mcdonald's in Problem 5.17. question has four choices. Assume that the student has no knowl- 5.17 In Example 5.4 that begins on page 186, you and two friends edge of the correct answers to any of the questions. She has decided decided to go to Wendy's. Now, suppose that instead you go to on a strategy in which she will place four balls (marked A, B, C, and Mcdonald's, which recently filled approximately 92.9% of the D) into a box. She randomly selects one ball for each question and orders correctly. What is the probability that replaces the ball in the box. The marking on the ball will determine a. all three orders will be filled correctly? her answer to the question. There are five multiple-choice questions b. none of the three will be filled correctly? on the exam. What is the probability that she will get c. at least two of the three will be filled correctly? a. five questions correct? d. What are the mean and standard deviation of the binomial b. at least four questions correct? distribution used in (a) through (c)? Interpret these values. c. no questions correct? e. Compare the results of (a) through (d) with those of Burger King d. no more than two questions correct? in Problem 5.16 and Wendy's in Example 5.4