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- Leo is a very average golfer. The probability that he hits a bad shot at any time is 0.4, independent of the outcome of any other shot. In a round of golf, the probability that Leo's first bad shot is his fifth shot is Select one: O (0.4) (0.6)' O (0.4)5 O (0.6)* (0.4)' O (0.6) (0.4)'Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p' for the population proportion, whichever symbols you need of " "not" and express any values as a fraction e.g. p = 1/3) Ho = H₂ = (b) Now suppose Matt makes n = 38 rolls, and a 2 comes up 8 times out of the 38 rolls. Determine the P-value of the test: P-value= (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No)A = 11 B = 2 C= 2 D = 0 F = 1 105, 82, 94.5, 72.5, 92, 91, 52, 86, 100, 96, 98, 109, 96, 98, 95, 72
- If a number is randomly chosen from the interval (-3,3). What is the probability that the number is less than −8/3? Suppose that a number is randomly chosen from the interval (-6,2). What is the probability that the number chosen within 2 units away from 1? NOTE: ROUND OFF your answer to FOUR DECIMAL places.The probability that a student passes APPDA is 2/3, and the probability that she passes Research Methods is 4/9. If the probability of passing at least one course is 4/5, what is the probability that she will pass both courses ? Final answer in % and 2 decimal places.You're on our way to earn a degree. In one of your courses, you need to pass an exam once to pass the class. The probability that it’d take you at most 6 attempts to pass the exam for once is 728⁄729. Calculate the probability that it would take you more than 3 attempts to pass the exam for once given that you can taake as many attempts as you need.For every attempt, the probability of passing the exam is constant.
- A farmer only grows apple and orange trees in his orchard. 40% of his trees are apple trees. He is concerned that a parasite may be infecting his trees. The probability of the parasite infecting a given apple tree is 5% and the probability of the parasite infecting a given orange tree is 3%. Please give your answers to 3 decimal places, for example 0.305. a) What proportion of his trees are infected by the parasite? Your answer is 1 b) If a given tree is not infected, what is the probability that this tree was an apple tree? Your answer isThe probability of a person selling by phone to sell for each call is independent of each other and is 0.2. So, what is the probability that he did not sell in exactly 5 calls before making the second sale?Ezra buys a bag of cookies that contains 9 chocolate chip cookies, 7 peanut butter cookies, 4 sugar cookies and 4 oatmeal cookies.What is the probability that Ezra reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie? Give your answer as a fraction, or accurate to at least 4 decimal places.
- The number of work accidents that occur per week in a mine follows Poisson's law so that the probability of 2 accidents occurring is equal to 3/2 of the probability of an accident occurring. Calculate the probability that the time for the first accident to occur is one week.A bag contains (x + 1) yellow balls, x black balls and (x – 1) white balls. Probability of getting a yellow ball is (2/15) more than that of getting a white ball. Find the value of x.Charlie is about to take two laps in the school swimming pool. The time of his first lap is X minutes, where X is an Exponential(1) random variable. The time of his second lap is Y minutes, where Y is an Exponential(X) random variable. What is the probability that he completes his second lap within one minute?