Question 1POST OFFICEAccording to a USPS study, the weight of a randomly selected shipment box has unknown distribution with amean of 22.7 lbs and a standard deviation of 4.5 lbs. Let X be the weight of a randomly selected shipmentbox and let S be the total weight of a random sample of size 9.1. Describe the probability distribution of X and state its parameters and o:✓x (μ=X~N22.70 4.52. Explain why the Central Limit Theorem cannot be usedTand find the probability that the weight of a randomly selected shipment box is between 12 and 13 lbs.0.0069 X (Round the answer to 4 decimal places)the original population is normally distributed although the sample size is small (n<30)

Given that the weight of a randomly selected shipment box has unknown distribution with a mean of…

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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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Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviation of σ=12.5 beats per minute If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.
An elevator has a placard stating that the maximum capacity is 1860 lb—12 passengers. So, 12 adult male passengers can have a mean weight of up to 1860/12=155 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 155 lb. (Assume that weights of males are normally distributed with a mean of 162 lb and a standard deviation of 31 lb.) The probability the elevator is overloaded is
An elevator has a placard stating that the maximum capacity is 3900 lb-26 passengers. So, 26 adult male com passengers can have a mean weight of up to 3900/26= 150 pounds. Assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 39 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 150 lb. b. Find the probability that a sample of 26 randomly selected adult males has a mean weight greater than 150 lb. c. What do you conclude about the safety of this elevator? *** a. The probability that 1 randomly selected adult male has a weight greater than 150 lb is 0.5319 (Round to four decimal places as needed.)
A prototype automotive tire has a design life of 38,500 miles with a standard deviation of 2,500 Five such tires are manufactured and tested. On the assumption that the actual population mean is 38,500 miles and the actual population standard deviation is 2,500 miles, find the probability that the sample mean will be less than 35,000 miles. Assume that the distribution of lifetimes of such tires is normal. A normally distributed population has mean 1,200 and standard deviation Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300. Find the mean and standard deviation of X for samples of size Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100 and 1,300. Scores on an entrance exam in a large university, freshman course are normally distributed with mean 72.5 and standard deviation 13.0. Find the probability that the score X on a randomly selected exam paper is between 70…
Two devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
The lifetime of a particular component is normally distributed, with a mean of 1000 hours, and a standard deviation of 100 hours. Find the probability that a randomly-drawn component will last 930 hours or less.

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