A certain mechanical component is to be manufactured with a diameter of 3 centime-ters. The manufacturing process produces components whose diameters are normallydistributed with mean value = 3 and standard deviation is 0.02 cm.(a) What percentage of components will have a diameter greater than 3.045 cm?(b) What percentage of components with have a diameter less than 2.95 cm?(c) If the manufacturer discards any component with a diameter that differs from 3 cmby more than 0.03 cm (in either direction), then what percentage of componentswill be discarded?

Introduction: Denote X as the diameter of a randomly selected component. It is given that X has a…

Answered: A certain mechanical component is to be…

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 level of calcium in the blood of healthy young adults follows a normal distribution with mean u = 10 milligrams per deciliter and standard deviation s = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The sample mean of these 100 measurements is X = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this question, we perform the following hypothesis test: H0: u = 10, Ha: u < 10. What is the test statistic? (use two decimal places in your answer) What is the p-value equal to? At the 10% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT t the 5% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT
= 222 mg/dLi and Total cholesterol levels for middle aged men (aged 55 – 64) follow approximately a normal distribution with mean, µ standard deviation, o = 37 mg/dLi. Those with a total cholesterol of 240 mg/dLi or higher have "high" cholesterol (and have twice the risk of coronary heart disease as someone with a total cholesterol less than 200 mg/dLi) Find the Z-score (standard score) for an observation of 290 mg/dl.
The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o = 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 15 cigarettes of this brand. The sample yields an average of 1.6 mg of nicotine. Conduct a test using a significance level of a = 0.05. (a) The standardized test statistic (b) The critical value (endpoint of Rejection Region) is z* = (c) The final conclusion is OA. The nicotine content is probably higher than advertised. B. There is not sufficient evidence to show that the ad is misleading.
Suppose that the mean systolic blood pressure for women over age seventy is 131 mmHg (millimeters of mercury), with a standard deviation of 9 mmHg. Suppose that the blood pressures are normally distributed. Complete the following statements. (a) Approximately? mmHg and 140 mmHg. of women over seventy have blood pressures between 122 (b) Approximately 95% of women over seventy have blood pressures between mmHg and mmHg.
A certain variable has a bell-shaped distribution with mean μ=176.16μ=176.16 and standard deviation σ=4.9σ=4.9. You observe a value of x=184x=184. Is this a TYPICAL value of the variable (within 2 standard deviations of the mean), or an UNUSUAL one (more than 2 standard deviations from the mean)?
A random sample of 17 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 98.6 pounds with estimated sample standard deviation s1 = 5.6 pounds. Another sample of 26 adult male wolves from Alaska gave an average weight x2 = 88.2 pounds with estimated sample standard deviation s2 = 6.0 pounds. (a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem. μp μ1 – μ2p1 – p2 (b) Let μ1 represent the population mean weight of adult male wolves from the Northwest Territories, and let μ2 represent the population mean weight of adult male wolves from Alaska. Find a 99% confidence interval for μ1 – μ2. (Use 1 decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of…
Suppose that the TSH (Thyroid Stimulating Hormone) levels among healthy individuals are normally distributed with a mean of 3.2 units/mL. Suppose also that exactly 98% of healthy individuals have TSH levels below 6.1units/mL. Find the standard deviation of the distribution of TSH levels of healthy individuals. Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.
A normal population has a mean μ = 31 and standard deviation = 8. What proportion of the population is less than 29?

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