Problem 3. A study claims that 75% of children under the age of 13 in BritishColumbia have been vaccinated against the chicken pox. A survey of randomly se-lected residents of a certain city included 800 children who were under the age of 13.a) Does the distribution of P, the sample proportion of non-vaccinated children,have an approximate normal distribution? If so, what is its mean and standarddeviation?b) What is the approximated probability that sample proportion p is more than184/800?c) What is the probability that p lies within the interval from .23 to 37?d) Would the sample proportion value p= (0.37 contradict the reported value p ofthe study? Explain briefly.

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Answered: Problem 3. A study claims that 75% of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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3. Replacements times of TV sets are reported to follow a normal distribution having a mean of 8.5 years with standard deviation of 1.2 years. If 25 TV sets are selected, what is the probability that the replacement time is between 8.4 years and 9 years.
9. Women's heights are normally distributed with a mean of 63.8 in and standard deviation of 2.6 in. a) If one woman is randomly selected, find the probability that her height is less than 62.4 inches. b) If one woman is randomly selected, find the probability that her height is more than 64.5 inches. c) If one woman is randomly selected, find the probability that her height is between 61.0 inches and 68.0 inches. d) If 24 women are randomly selected, find the probability their mean height is less than 62.1 inches. e) Find P17.
4. Manufacturer A's television picture tubes have a mean lifespan of 7.3 years and a standard deviation of 0.57 years; while those of manufacturer B have a mean duration of 6.39 years and a standard deviation of 0.42 years. What is the probability that a random sample of 39 kinescopes from manufacturer A will have a mean lifespan that is 1 year less than the mean lifespan in a sample of 43 kinescopes from manufacturer B? Round your answer to four decimal places after the period.
14
20. Birth weights of babies born to full-term pregnancies follow roughly a normal distribution. At Asian Hospital, the mean weight of babies is 7 Ibs with a standard deviation of 14oz. (1 lb = 14 oz). What is the probability that a born baby weighs more than 7.5 Ibs? 0.65% 15.87% 12.65% 30.85%
3. The braking distance for a Krazy-Car traveling at 50 mph is normally distributed with a mean of 50 ft. and a standard deviation of 5 ft. Answer the following without using a calculator or a table. • What is the likelihood a Krazy-Car will take more than 65 ft. to stop? • What is the probability a Krazy-Car will stop between 45 ft. and 55 ft.? • What percent of the time will a Krazy-Car traveling at 50 mph stop between 35 and 55 ft.? • What is the probability a Krazy-Car will require less than 50 ft. or more than 60 ft. to stop?
4. According to a 2019 Federal Reserve report, 54% of U.S. young adults who went to college took on some debt for their education. Suppose we take a random sample of 400 U.S. young adults who went to college and took on some debt, a) Find the mean and standard of the sampling distribution of ?̂. mean= ?? = standard deviation of the sample proportion, ?? = b) Determine the probability that more than 60% of the persons in the sample took on some debt.
1. Stephen would like to check if his claim is true upon knowing that the average grade in Mathematics of his class is at least 85%. He got a sample from his classmates listed as follows: 93, 88 , 90,95 , 83, 85, 77 , 78 , 90, 80 a. What statistical tool is suited to determine if his class is true? Why? b. Assume that the distribution is normal, what would Stephen's conclusion be if the level of significance is 5%?
. The demand for high-grade gasoline at a service station is normally distributed with mean 27,009 gallons per day and standard deviation 4,530. Find two values that will give a symmetric 0.98 probability interval for the amount of high-grade gasoline demanded daily.
5. The ages of U.S. commercial aircraft have a mean of 13 years and a standard deviation of 7.9 years (based on data from Aviation Data Services). a. If the Federal Aviation Administration randomly selects 35 commercial aircraft for special stress tests, find the probability that the mean age of this sample group is greater than 15 years? b. If the Federal Aviation Administration randomly selects 42 commercial aircraft for special stress tests, what is the mean sample age of the aircraft for the top 75% of the sample?4
7) $40,000, with a standard deviation of $2000. Assuming that the distribution of income is (approximately) normal, what is the probability that a worker picked at random will have the annual income between $39,000 and $42,000 ? The mean annual income of a worker in a certain professional category is

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