Question 3Two methods have been developed to determine the nickel content of steel. Ina sample of five replications of the first method on a certain kind of steel, theaverage measurement (in percent) was = 3.16 and the standard deviationwas s, = 0.042. The average of seven replications of the second method wasỹ = 3.24 and the standard deviation was s = 0.048.a) Determine if there is a difference in the mean measurements betweenthe two method and explain the most likely assumption that could bemade before solving this problem?b) What informed your choice of solution method?c) In a sample of 100 newly manufactured automobile tires, 7 are found tohave minor flaws in the tread. If four newly manufactured tires areselected at random and installed on a car.Suggest a statistical method/formula to use if you want toestimate the probability that none of the four tires have a flaw?Define the random variable in the problem 3c) and hence, thedistribution of such random variable?ii.

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c) In a sample of 100 newly manufactured automobile tires, 7 are found to have minor flaws in the tread. If four newly manufactured tires are selected at random and installed on a car. Suggest a statistical method/formula to use if you want to estimate the probability that none of the four tires have a flaw? i. ii. Define the random variable in the problem 3c) and hence, the distribution of such random variable?

c) In a sample of 100 newly manufactured automobile tires, 7 are found to have minor flaws in the tread. If four newly manufactured tires are selected at random and installed on a car. Suggest a statistical method/formula to use if you want to estimate the probability that none of the four tires have a flaw? i. ii. Define the random variable in the problem 3c) and hence, the distribution of such random variable?

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.96 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.80 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.80 grams? Use α = 0.01. Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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