Two fair dice are rolled at once. Let X be the random variable that gives the difference in the number of dots that appear on the top faces of the two dice. Write down the (1) sample space and (2) range space. Construct its (3) probability mass function and compute for the (4) mean, (5) variance and (6) standard deviation.
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Two fair dice are rolled at once. Let X be the random variable that gives the difference in the number of dots that appear on the top faces of the two dice. Write down the (1)
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- The state of California has a mean annual rainfall of 19 inches, whereas the state of New York has a mean annual rainfall of 48 inches (Current Results website, October 27, 2012). Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with and (to decimals). b. What is the probability that the sample mean is within inch of the population mean for California? (to decimals) c. What is the probability that the sample mean is within inch of the population mean for New York? (to decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within inch of the population mean greater? Why? The probability of being within inch is greater because the sample size is .From a large consignment of clementine fruit destined for a UK supermarket the cus- toms office is making a check at the boarder. According to the sender the weight of the fruit belongs to an unknown distribution of mean 50 g and variance 16 g. If the cus- toms officer takes 100 fruits at random what is the probability that their total weight will be more than 5040 g. Justify any assumptions you make in your calculations.You decided to plant roses. The probability that a planted roses seedgerminates is 0.80. You plant nine seeds and let the binomial random variable X denotes the number ofroses seeds that successfully germinate. What is the average number of roses you could expect togerminate? What is the variance and standard deviation of X?
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.4 minutes and a standard deviation of 3.3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 38 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The burning life (in hours) of electric lamps installed in a street of a city follows a normal distribution with an average of 120 burning hours and variance of 54000 square minutes. Find the probability of the electric lamps that are likely to burn for more than 110 hours more than 5124 minutes and less than 7450 minutes17 percent of U.S. employees who are late for work blame oversleeping. You randomly select four U.S. employees who are late for work and ask them whether they blame oversleeping. The random variable represents the number of U.S. employees who are late for work and blame oversleeping. Find the mean of the binomial distribution. μ=
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 3.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)Find the variance of x or the number of cups of coffee. (Do not round intermediate steps but round your final answer to 4 decimal places)The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 2.5minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
- The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.2 minutes and a standard deviation of 3.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.7 minutes and a standard deviation of 3.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)The 5 crew members of the exploration team of the spaceship Enterprise under the command of Captain Kirk are 162, 172, 177, 180 and 184 cm in height, respectively. Calculate the expected value and variance of the height of a randomly selected person among these 5 crew members. ( explaining them to someone who does not know anything about the subject)
