3. There are 10 distinct pairs of socks in my drawer, all mixed up. What is the probability that I can form a complete pair' by picking four socks at random? Find the distribution function of the number of complete pairs.
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- You might think that if you looked at the first digit in randomly selected numbers that the distribution would be uniform. Actually, it is not! Simon Newcomb and later Frank Benford both discovered that the digits occur according to the following distribution: (digit, probability)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046)(1,0.301),(2,0.176),(3,0.125),(4,0.097),(5,0.079),(6,0.067),(7,0.058),(8,0.051),(9,0.046) The IRS currently uses Benford's Law to detect fraudulent tax data. Suppose you work for the IRS and are investigating an individual suspected of embezzling. The first digit of 122 checks to a supposed company are as follows: Digit 1 2 3 4 5 6 7 8 9 ObservedFrequency 29 20 9 9 7 6 19 14 9 a. State the appropriate null and alternative hypotheses for this test.b. Explain why α=0.01α=0.01 is an appropriate choice for the level of significance in this situation. c. What is the P-Value? Report answer to 4 decimal placesP-Value =…3. From a box containing four 10-peso coins and two 5-peso coins, 3 coins are selected at random without replacement. Determine the cumulative distribution function of the random variable representing the number of 10-peso coins. IIt is known that the customers of a hotel are 0.68 percent satisfied with the hotel. Accordingly, what is the probability of asking 10 people about their satisfaction level so that satisfied customers can be selected from 10 hotels?
- Please show work... and round probabilities to FOUR DECIMALS The following table summarizes results from 985 pedestrian deaths that were caused by accidents. Pedestrian Pedestrian was NOT Intoxicated intoxicated Driver was intoxicated 59 79 Driver was NOT 266 581 intoxicated If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. If two DIFFERENT pedestrian deaths are randomly selected, find the probability that they both involve intoxicated pedestrians. If we randomly select a pedestrian death, what is the probability that the pedestrian was intoxicated, given that the driver was intoxicated? If we randomly select a pedestrian death, what is the probability that the driver was intoxicated?) The percentage of students at a college that have internet connection at home is 80%. In a random sample of 152 students, what is the probability that more than 38 students have the internet connection at homeAccording to the statistics, 13% of cars in the city were at least 12 years old in2004. Assume that this result holds true for the current population of all cars in thecity. Random sample of 500 cars are selected at random. Approximate the probabilitythat 80 to 98 cars are at least 12 years old?
- In principle, a distribution of means can be formed by?pls helpSuppose you are going to draw 20 cards, with replacement, from a deck of 52 cards and record the proportion of draws that are red. There are 26 red and 26 black cards in a typical deck of cards. You draw the 20 cards, replacing each card between draws, and 2/20 cards drawn are red. Are you suspicious about the fairness of this deck of cards? Simply list the answer to your probability calculation and explain your reasoning.
- A group of botanists is studying the distribution of carnations in a field. The field is divided into a number of equal sized squares. The mean number of carnations per square is assumed to be 3. The carnations are distributed randomly throughout the field. Find the probability that: (b) (i) there will be more than two carnations. (ii) either five or six carnations.4 For this problem, assume there are 10 adjacent seats in a row. How many different ways can 10 people be seated in them?Anita's, a fast-food chain specializing in hot dogs and garlic fries, can monitor how many customers at its restaurants want to eat (in addition to ordering takeout) to decide whether or not to build a location to play in the city. . Including the presence of Sammy the mascot in local locations, stores and franchises, Anita reports that 45% of her customers order food for delivery. If this ratio is true, what is the probability that a random sample of 3 of Anita's 4 customers will order food? Round your response to at least three decimal places. (If necessary, consult a list of formulas.)