Problem 4 | The daily revenue of an online retailer has mean 20 and variance 400. (i) Find the lowest possible upper bound on the probability that the daily revenue exceeds 80.
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- The quality control manager at a company manufacturing company believes that the mean life of a computer is 81 months with a variance of 64. If he is incorrect what is the probability that the mean of a sample of 58 computers would differ from the population mean by less than 2.79 months round your answer to 4 decimal placesFor a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 510 and a standard deviation of 175. The grading process of this year's exam has just begun. The mean score of the 40 exams graded so far is 530. What is the probability that a sample of 40 exams will have a mean score of 530 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places. 0 SThe mean points obtained in an aptitude examination is 179points with a variance of 225. What is the probability that the mean of the sample would differ from the population mean by less than 2.5 points if 77exams are sampled? Round your answer to four decimal places.
- A normally distributed random variable has a mean of 449. If a score of 433 lies two standard deviations below the mean, find the variance of X.Suppose the horses in a large stable have a mean weight of 873lbs, and variance of 17,161. What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 50 horses are sampled at random from the stable? Round your answer to four decimal places.Suppose that home prices (in thousands of dollars) in a certain region have a mean of 360 and a standard deviation of 180. A realtor randomly selects a sample of 90 homes in the region. Estimate the probability that the sample mean home price from the realtor's data is greater than 400 (thousand dollars). You must justify your solution, and note any assumptions you are making.
- Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be positive. Round your answer to at least four decimal places.If Y is a random variable with a mean of 30 and a standard deviation of 10, what is the probability that Y is between 35 and 40?Justin and Robbie are golfers. The distribution of Justin's golf scores has a mean of 225 and a standard deviation of 25. Robbie's golf score distribution has a mean of 240 and a standard deviation of 15. Both distributions are approximately normal and they are completely independent of each other. What is the closest probability that Justin will have a higher golf score than Robbie in a randomly selected golf round?
- The cost of 5 gallons of ice cream has a variance of 49 with a mean of 36 dollars during the summer. What is the probability that the sample mean would differ from the true mean by less than 1.5 dollars if a sample of 142 5-gallon pails is randomly selected? Round your answer to four decimal places.The variance of the scores on a skill evaluation test is 203,401 with a mean of 1469 points. If 358 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 41 points? Round your answer to four decimal places.A professor know that her statistics students' final exam scores have a mean of 79 and a standard deviation of 12.8. In his class, an "A" is any exam score of 90 or higher. This quarter she has 23 students in her class. Wht is the probability that 6 students or more will score an "A" on the final exam?