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Let A and B be events with P (A) =0.3, P (B) =0.4, and P(A and B) =0.2. (a) Are A and B independent? Explain. (b) Compute P (A or B). (c) Are A and B mutually exclusive? Explain. Part: 0 / 3 Part 1 of 3 (a) Are A and B independent? Explain. The events A and B (Choose one) V independent since (Choose one) P(A) .P(B) = P(A and B X P(A) .P(B) + P(A and B) P (A and B) #0 P (A and B) = 0How are your grades? In a recent semester at a local university, 400 students enrolled in both Statistics I and Psychology I. Of these students, 87 got an A in statistics, 71 got an A in psychology, and 41 got an A in both statistics and psychology. Round the answers to four decimal places, as needed. Part 1 of2 (a) Find the probability that a randomly chosen student got an A in statistics or psychology or both. The probability that a randomly chosen student got an A in statistics or psychology or both is l '. Part2 of2 (b) Find the probability that a randomly chosen student did not get an A in statistics. The probability that a randomly chosen student did not get an A in statistics is l l. Genetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places. Gene 2 Dominant Recessive Dominant 60 20 Gene 1 Recessive 13 7 Send data to Excel (a) What is the probability that in a randomly sampled individual, gene 1 is dominant? (b) What is the probability that in a randomly sampled individual, gene 2 is dominant? (c) Given that gene 1 is dominant, what is the probability that gene 2 is dominant? (d) Two genes are said to be in linkage equilibrium if the event that gene 1 is dominant is independent of the event that gene 2 is dominant. Are these genes in linkage equilibrium? Do you know Squidward? According to a survey by Nickelodeon TV, 92% of children under 13 in Germany recognized a picture of the cartoon character SpongeBob SquarePants. Assume that among those children, 74% also recognized SpongeBob's cranky neighbor Squidward Tentacles. What is the probability that a German child recognized both SpongeBob and Squidward? Write your answer as a fraction or a decimal, rounded to four decimal places. The probability that the German child recognized both SpongeBob and Squidward is DOThe probability that a certain make of car will need repairs in the first seven months is 0.5. A dealer sells seven such cars. What is the probability that at least one of them will require repairs in the first seven months? Round your final answer to four decimal places. P(At least one car will require repairs) =' ' X S Playing the horses: In horse racing, one can make a trifecta bet by specifying which horse will come in first, which will come in second, and which will come in third, in the correct order. One can make a box trifecta bet by specifying which three horses will come in first, second, and third, without specifying the order. Part 1 of2 (a) In an eighthorse field, how many different ways can one make a trifecta bet? There are l ' ways to make a trifecta bet. X S Part2 of2 (b) In an eighthorse field, how many different ways can one make a box trifecta bet? There are l ' ways to make a box trifecta bet. X 5) Determine whether the random variable described is discrete or continuous. The weight of a randomly chosen college student. The random variable described is (Choose one) V . Standardized Test: You are trying to answer a multiple choice question on a standardized test. There are five choices. If you get the question right, you gain 1 one point, and if you get it wrong, you lose point. Assume you have no idea what the right answer is, so you pick one of the choices at random. What is the 3 expected value of the number of points you get? What is the expected value of the number of points you get? Round the answer to two decimal places. The expected value of the number of points you get is l I. X 5) College bound: A national college researcher reported that 64% of students who graduated from high school in 2012 enrolled in college. Twenty seven high school graduates are sampled. Part 1 of2 (a) What is the mean number who enroll in college in a sample of 27 high school graduates? Round the answer to two decimal places. The mean number who enroll in college in a sample of 27 high school graduates is i i. X 53 Part 2 of2 (b) What is the standard deviation of the number who enroll in college in a sample of 27 high school graduates? Round the answer to four decimal places. The standard deviation of the number who enroll in college in a sample of 27 high school graduates is i i. X E) Find each of the shaded areas under the standard normal curve using a TI-84 calculator. Round the answers to four decimal places. Part 1 of4 1.03 The area of the shaded region is l '. Part 2 of4 /i\\ Part 2 of4 -1.92 The area of the shaded region is ' '. Part 3 of4 1.26 0.64 The area of the shaded region is i '. Part 4 of4 0.32 1.32 The area of the shaded reqion is | |. _ Use Excel to nd the zscore for which the area to its left is 0.76. Round the answer to two decimal places. The zscore for the given area is l l. Use Excel to nd the zscore for which the area to its right is 0.61. Round the answer to two decimal places. The zscore for the given area is i i. Use Excel to nd the zscores that bound the middle 68% of the area under the standard normal curve. Enter the answers in ascending order. Round the answers to two decimal places. The zscores for the given area are l:l and l:l. Big chickens: The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1446 grams and standard deviation 180 grams. Use the TI84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1185 and 1286 grams? (b) What is the probability that a randomly selected broiler weighs more than 1551 grams? (c) Is it unusual for a broiler to weigh more than 1800 grams? Round the answers to at least four decimal places. Big chickens: A report from a poultry industry news Web site stated that the weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1446 grams and standard deviation 180 grams. Use the TI84 PLUS calculator and round your answers to at least two decimal places. (a) Find the 35th percentile of the weights. (b) Find the 92"d percentile of the weights. (c) Find the second quartile of the weights. (d) A chicken farmer wants to provide a moneyback guarantee that his broilers will weigh at least a certain amount. What weight should he guarantee so that he will have to give his customers' money back only 1% of the time