You may need to use the appropriate appendix table or technology to answer this question.The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 35 years of rainfall forCalifornia and a sample of 45 years of rainfall for New York has been taken.(a) Describe the probability distribution of the sample mean annual rainfall for California by specifying its distribution form and parameters. (Round your answers to four decimal places as needed.)This is a normaldistribution with E(x) = 22✓and a-= 0.6761(b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)(c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)(d) In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?O part (c), because the population standard deviation is smallerO part (c), because the sample size is largerO part (b), because the standard error is smallerO part (b), because the population standard deviationsmaller

Note :As per the Bartleby guildlines we have to solve first three subparts and rest can be…

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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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An online retailer operates two independent warehouses (A & B) where it keeps its inventory. Each warehouse has a .05 probability of experiencing a fire. If a fire is experienced in a given warehouse, $1,000 in inventory will be lost. What is the pooled standard deviation of the warehouses per warehouse (round to the nearest whole number)?
You may need to use the appropriate appendix table or technology to answer this question. A group conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $23,858. Assume that the cost of a wedding is normally distributed with a mean of $23,858 and a standard deviation of $5,600. (a) What is the probability that a wedding costs less than $18,000? (Round your answer to four decimal places.) (b) What is the probability that a wedding costs between $18,000 and $32,000? (Round your answer to four decimal places.) (c) What is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (Round your answer to the nearest dollar.) $_______________
Suppose that the walking step lengths of adults are normally distributed with a mean of 2.4 feet and a standard deviation of 0.3 feet. A sample of 34 step lengths is taken. Find the probability that the mean of the sample taken is more than 2.5 feet. Your answer should be from the cumulative normal distribution table.
Suppose that you are studying the number of vehicles owned by a US household. You find that the average is 1.9 vehicles per household with a standard deviation of 2.8 vehicles per household. What is the most likely shape for the population described above? Find the probability that 40 randomly selected households have an AVERAGE number of vehicles greater than 2.5.
Sadie deals 5 cards from a standard deck of 52 cards. She would like to deal as many spades as possible. Is it reasonable to approximate this distribution with a normal distribution? Give a reason.
One year, the distribution of salaries for professional sports players had a mean of $1.6 million and a standard deviation of $0.7 million. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players that year exceeds $1.1 million.
The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 40 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. (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (c) What is the probability that the sample mean is within 1 inch of the population mean for New York?.
Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?
The board of examiners that administers the real estate broker’s examination in a certain state found that the mean score on the test was 450 and the standard deviation was 50. If the board wants to set the passing scores so that only the top 5% of all applicants pass, what should the passing score be? Assume that the scores are normally distributed.
You may need to use the appropriate appendix table or technology to answer this question. The weight of football players is normally distributed with a mean of 220 pounds and a standard deviation of 20 pounds. What is the probability of a player weighing less than 255 pounds
The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?
You may need to use the appropriate appendix table or technology to answer this question. A group conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is $24,858. Assume that the cost of a wedding is normally distributed with a mean of $24,858 and a standard deviation of $5,600. (a) What is the probability that a wedding costs less than $19,000? (Round your answer to four decimal places.) (b) What is the probability that a wedding costs between $19,000 and $31,000? (Round your answer to four decimal places.) (c) What is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (Round your answer to the nearest dollar.)

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