We measured the length of two sides X and Y of a rectangular plate several times under fixedcondition. We ignored the accuracy of the measurement instrument. The measurement resultsinclude the mean X = 10 in, the standard deviation of the X = 1.1 in, and the mean Y = 15 in, thestandard deviation of the Y= 1.3 in, each measurement were collected 40 times. Please estimate thenearest uncertainty of the area A = XY at probability of 95%.O 12O 24O 10O all solutions are not correct

Answered: Image /qna-images/answer/1f3a8317-1072-4fb5-9e5e-3a990c81031b.jpg

Answered: We measured the length of two sides X…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The mean weight of all Goliath grouper caught on the Treasure coast is 367 pounds, with a standard deviation of 33 pounds. Suppose a random sample of 32 Goliath Grouper from the Treasure Coast are caught and weighed. Determine the probability that the average weight of the sample of 32 Goliath Grouper is within 7 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places , if necessary .
The capacitance of capacitors produced by a machine is approximately normally distributed with a mean of µ = 1000 µF and a standard deviation of 80 µF. A sample of 16 capacitors is taken and the average of the capacitances values is computed. Based from the manufacturer’s standards, the machine is working properly if the computed average capacitance falls within 950 µF and 1050 µF. Otherwise, we conclude that µ ≠ 1000 µF. a.) Determine the probability of committing a type I error when µ = 1000 µF.b.) Determine the probability of committing a type II error when µ = 1080 µF. Hint: Use the sampling distribution of the mean when computing the probabilities
The compressive strength of concrete is normally distributed with mean 2500 psi and standard 50 psi. Find the probability that a random sample of n=5 specimens will have a sample mean diameter that falls in the interval from 2499 psi to 2510 psi. Answers in 4 significant figures.
The weight of a random person is normally distributed, with a mean of 62 kg and variance of 15 kg2. What is the probability that a random person's height is over 58 kg? Please round your result to two decimal places, and use the z-table.
The mean hemoglobin level in the blood for a certain large group of individuals is 21.0 grams per milliliter (g/ml). The standard deviation is 2 g/ml. If a sample of 25 individuals is selected, find the probability that the mean will be greater than 21.3 g/ml. Assume that the variable is normally distributed.
The mean weight of 800 male students at a certain college is 70kg and the standard deviation is 10kg assuming that the weights are normally distributed find how many students weigh i) Between 60 and 78kg ii) more than 82kg.
The average diameter of a sand dollar on a certain island is 3.50 centimeters with a standard deviation of 1.00 centimeters. If 25 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.28 centimeters. Assume that the variable is normally distributed.
The existing machine setting of a factory produces bearings with a diameter that is normally distributed with mean and standard deviation equal to 3.0005 cm and 0.0010 cm, respectively. Customer specifications require the bearing diameters to lie in the interval [2.998, 3.002]. Those outside the interval are considered scrap and must be re-machined. With the existing machine selling, what fraction of total production will not be considered scrap?
The lengths of nails manufactured at a factory are normally distributed with a mean length of 4.43 cm and a standard deviation of 1.41 cm. For quality control purposes, a random sample of 14 nails is chosen once per day, and measured. Let X be the random variable representing the mean length of the nails. A. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of _______cm and a standard error of the mean________cmb. Find the z-score associated to a sample with a mean of 4.56 cm, using the sampling distribution. Round your answer to two decimal places. ______c. Find the probability that a randomly selected sample of 14 nails has a mean length higher than 4.56 cm. Round your answer to 4 decimal places.________
The mean inside diameter of a washer produced by a machine is 0.502 inches and the standard deviation is 0.005 inches. The purpose for which these washers are intended allows a maximum tolerance in the diameter of 0.496 to 0.508 inches, otherwise the washers are considered defective. Assuming the diameters are normally distributed, find:a. The probability that the inside diameter of a randomly chosen washer is less than 0.515 inches b. The probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches
A sample of 200 whatzits is chosen at random from the day's production and it is found that 180 meet specifications. a. Estimate the proportion of the day's production that meets specifications and give the uncertainty of the estimate. b. What sample size is necessary to arrive an estimate with uncertainty of less than 0.001?
According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.12°F and a standard deviation of 0.65°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?

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