Suppose that the test score of a student taking the final of a probability course is a random variable with mean 68.9. (a) Give an upper bound for the probability (in three decimal places) that the student's test score will exceed 95.
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- 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.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 number of automobile sold weekly at a certain dealership is a random variable with expected value 16.Give an upper bound to the probability that the next week sales exceed 18.
- Suppose that from the past experience a professor knows that the test score of a student taking his final examination is a random variable with mean 61 and a standard deviation 8.5. how many students would have to take the examination to ensure, with probability at least 0.94, that the class average would be within 3 of 61?A certain type of cancer is known to exist in 2 percent of the population of the males in their fifties. A test for the disease has been is advertised by a pharmaceutical company to have sensitivity 0.97 and specificity 0.95. A male is randomly selected from this population, and tested. The test result is negative. First determine the probability this male has the cancer.The average time a CEO remains in office for a certain company is 3.6 years; then a new CEO is selected. It seems that the length of time in office of each CEO is quite unpredictable. What is the standard deviation, in years, of the time until we must find the 6th CEO. What is the probability that no more than 2 CEO's will leave office in the next 5 years?
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