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- In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 6.1 inches.A) What is the probability that a randomly chosen child has a height of less than 42.95 inches?Answer=____ (Round your answer to 3 decimal places.)B) What is the probability that a randomly chosen child has a height of more than 70.3 inches?Answer=____ (Round your answer to 3 decimal places.)The amount of pollutants that are found in waterways near large cities is nomally distributed with mean 8.7 ppm and standard deviation 1.8 ppm. 40 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the probability that one randomly selected city's waterway will have more than 7.7 ppm pollutants? b. For the 40 cities, find the probability that the average amount of pollutants is more than 7.7 ppm. c. For part b, is the assumption that the distribution is normal necessary? O NoO Yes d. Find the IQR for the average of 40 cities. Round to two decimal places. Q1 = ppm Q3 = ppm IQR: ppmThe United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations. a. What is the probability that all six arrive within two days? (0.7351) b. What is the probability that exactly five arrive within two days? (0.2321) c. Find the mean number of letters that will arrive within two days. (5.7) d. Compute the variance and standard deviation of the number that will arrive within two days.(var=0.285)
- I need help on all three parts please!!A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 12,640 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 12,640 children. b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 12,640 children is 0 or 1. c. What is the probability of more than one case? d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this tumor occurred in a certain town, which had 17,151 children. a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of 17,151 children b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of 17,151 children is 0 or 1. C. What is the probability of more than one case? d. Does the cluster of four cases appear to be attributable to random chance? Why or why not? a. The mean number of cases is Type an integer or decimal rounded to three decimal places as needed.) b. The probability that the number of cases is exactly 0 or 1 is (Round to three decimal places as needed.) c. The probability of more than one case is (Round to three decimal places as needed.) d. Let a probability of 0.05 or less be very small," and let a probability of 0.95 or more be very large". Does the cluster of four cases…
- The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.5 ppm and standard deviation 1.4 ppm. 18 randomly selected large cities are studied. Round all answers to two decimal places. A.X-NO B. For the 18 cities, find the probability that the average amount of pollutants is more than 9 ppm. C. What is the probability that one randomly selected city's waterway will have more than 9 ppm pollutants? D. Find the IQR for the average of 18 cities. Q1 = Q3 = IQR:In sample standard deviation,(n - 1) is called degree of freedom, why?In the field of accountancy, times spent studying by students in the week before professional exams follow a Normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. a) What is the probability that the sample mean exceeds the population mean by more than 2 hours? b) What is the probability that the sample mean differs from the population mean by more than 4 hours? c) Suppose that a second (independent) random sample of 10 students was taken. Without doing any calculations, state whether the probabilities in parts (a) and (b) would be higher, lower or the same for the second sample.
- A recent study showed that 71% of adults need some type of corrective lens (glasses or contacts). A. If I grab a 6 random people what is the probability that fewer than 4 need corrective lenses? B. If I take a random sample of 2000 people what is the mean and standard deviation of the number of people who need corrective lens? C. Use the normal approximation to the binomial to find the probability that I get 1375 or fewer people who need corrective lenses out of a random sample of 2000. Illustrate what you are finding on a sketch of the normal curve and show your work.The healing time for a broken clavicle is from a Normal distribution with a mean of 41 days and a standard deviation of 6 days. What’s the probability a clavicle will heal... 16) in under 32 days? 17) in over 47 days? 18) in between 35 and 44 days? HELP ME OUTneed correctly
