Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses accommodated on any trip is independent of the number of cars on the trip. Suppose that X and y have the probability distributions shown below. x 0 1 2 3 4 5 p(x) 0.03 0.11 0.23 0.33 0.19 0.11 y 0 1 2 p(y) 0.45 0.10 0.45 (a) Calculate the mean of x. Calculate the standard deviation of X. (Round the answers to three decimal places.) (b) Calculate the mean of y. Calculate the standard deviation of y. (Round the answers to three decimal places.) The article "Should You Report That Fender-Bender?"'l' reported that 7 in 10 auto accidents involve a single vehicle. Suppose 15 accidents are randomly selected. (Round your answers to three decimal places.) USES (a) What is the probability that exactly five involve a single vehicle? (b) What is the probability that at most five involve a single vehicle? (c) What is the probability that exactly eight involve multiple vehicles? A certain company provides news for the information security community. In an article published by the company it reported that based on a large international survey of internet users, 70% of internet users have installed security solutions on all of the devices they use to access the internet. Igu SA (a) Suppose that the true proportion of internet users who have security solutions on all of the devices they use to access the internet is 0.70. If 20 internet users are selected at random, what is the probability that more than 10 have security solutions installed on all devices used to access the internet? (Round your answer to three decimal places.) (b) Suppose that a random sample of 20 internet users is selected. which is more likelyithat more than 15 have security solutions on all devices used to access the internet or that fewer than 5 have security solutions on all devices used to access the internet? Justify your answer based on probability calculations. (Round your answers to three decimal places.) Since the probability that more than 15 have security solutions on all devices is l land the probability that fewer than 5 have security solutions on all devices is l l , therefore lmorelhan 15 Vl \\/ having security solutions is more likely. Industrial quality control programs Often include inspection of incoming materials from suppliers. If parts are purchased in large lots, a typical plan might be to select 20 parts at random from a lot and inspect them. A lot might be judged acceptable if one or fewer defective parts are found among those inspected. ClthenNise, the lot is rejected and returned to the supplier. Use technology or SALT to find the probability of accepting lots that have each of the following. (Hint: Identify success with a defective part. Round your answers to three decimal places.) IQ USE (a) 5% defective parts P(lot will be accepted) = I (b) 20% defective parts P(lot will be accepted) : I (c) 30% defective parts P(lot will be accepted) = I Sophie is a dog that loves to play catch. Unfortunately, she isn't very good, and the probability that she catches a ball is only 0.3. Let x be the number of tosses required until Sophie catches a ball. (a) Does X have a binomial or a geometric distribution? 0 binomial O geometric (b) What is the probability that it will take exactly three tosses for Sophie to catch a ball? (c) What is the probability that more than 4 tosses will be required? | l You may need to use the appropriate technology to answer this question. Determine the following standard normal (2} curve areas. [Round your answers to four decimal places.) I USE SALT (a) the area under the 2 curve between 2.23 and 0.54 (b) the area under the 2 curve between 2 and 2 (c) the area under the 2 curve between 5 and 5 Let z denote a random variable having a normal distribution with u = 0 and o = 1. Determine each of the following probabilities. (Round your answers to four decimal places.) LA USE SALT (a) P(-0.86 - 1.35) = (d) P(z 2.60) =Determine the value of 2* such that it satisfies the conditions below. (Round your answer to two decimal places.) Ia USE SALT (a) 2* and 2* separate the middle 96.6% of all 2 values from the most extreme 3.4%. 2* =|2.12 Iy (b) 2* and 2* separate the middle 85.3% of all 2 values from the most extreme 14.7%. 2* =|1.75 lx (c) 2* and 2* separate the middle 97% of all 2 values from the most extreme 3%. 2* = |2.29 lx (d) 2* and 2* separate the middle 82% of all 2 values from the most extreme 18%. 2* =|1a1 |x Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean u = 6 ml and standard deviation o = 0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round your answers to four decimal places.) LO USE SALT (a) P(x 5.7) = 2.5 X (f) P(x > 5) = 1The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated by a normal distribution with a mean value of 115 seconds and a standard deviation of 15 seconds. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.) LO USE SALT 134 x seconds or less