A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 8, Problem 8.18P
Repeat part (a) of Problem 8.2 when it is known that the variance of a students test score is equal to 25.
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8.1.13 WP GO Tutorial An article in the Journal of Agricultural
Science ["The Use of Residual Maximum Likelihood to Model
Grain Quality Characteristics of Wheat with Variety, Climatic
and Nitrogen Fertilizer Effects” (1997, Vol. 128, pp. 135–142)]
investigated means of wheat grain crude protein content (CP) and
Hagberg falling number (HFN) surveyed in the United Kingdom.
The analysis used a variety of nitrogen fertilizer applications (kg
N/ha), temperature (°C), and total monthly rainfall (mm). The
following data below describe temperatures for wheat grown at
Harper Adams Agricultural College between 1982 and 1993. The
temperatures measured in June were obtained as follows:
15.2
14.2
14.0
12.2
14.4
12.5
14.3
14.2
13.5
11.8
15.2
Assume that the standard deviation is known to be σ = 0.5.
a. Construct a 99% two-sided confidence interval on the
mean temperature.
b. Construct a 95% lower-confidence bound on the mean
temperature.
c. Suppose that you wanted to be 95% confident that…
8.1.1 WP For a normal population with known variance σ²,
answer the following questions:
-
a. What is the confidence level for the interval x — 2.140/
√√n≤≤+2.140/√√n?
8.1.8 A civil engineer is analyzing the compressives trength of concrete. Compressive strength is normally distributed with σ2 = 1000(psi)2. A random sample of 12 specimens has a mean compressive strength ofx = 3250 psi.
a. Construct a 95% two-sided confidence interval on mean
compressive strength.
b. Construct a 99% two-sided confidence interval on mean
compressive strength. Compare the width of this confidence
interval with the width of the one found in part (a).
8.1.9Suppose that in Exercise 8.1.8 it is desired to estimate
the compressive strength with an error that is less than 15 psi at
99% confidence. What sample size is required?
Chapter 8 Solutions
A First Course in Probability
Ch. 8 - Suppose that X is a random variable with mean and...Ch. 8 - From past experience, a professor knows that the...Ch. 8 - Use the central limit theorem to solve part (c) of...Ch. 8 - Let X1,...,X20 be independent Poisson random...Ch. 8 - Fifty numbers are rounded off to the nearest...Ch. 8 - A die is continually rolled until the total sum of...Ch. 8 - A person has 100 light bulbs whose lifetimes are...Ch. 8 - In Problem 8.7, suppose that it takes a random...Ch. 8 - If X is a gamma random variable with parameters...Ch. 8 - Civil engineers believe that W, the amount of...
Ch. 8 - Many people believe that the daily change of price...Ch. 8 - We have 100 components that we will put in use in...Ch. 8 - Student scores on exams given by a certain...Ch. 8 - A certain component is critical to the operation...Ch. 8 - An insurance company has 10.000 automobile...Ch. 8 - A.J. has 20 jobs that she must do in sequence,...Ch. 8 - Redo Example 5b under the assumption that the...Ch. 8 - Repeat part (a) of Problem 8.2 when it is known...Ch. 8 - A lake contains 4 distinct types of fish. Suppose...Ch. 8 - If X is a nonne9ative random variable with mean...Ch. 8 - Let X be a nonnegative random variable. Prove that...Ch. 8 - Prob. 8.22PCh. 8 - Let X be a Poisson random variable with mean 20....Ch. 8 - Prob. 8.24PCh. 8 - If X has variance 2, then , the positive square...Ch. 8 - If X has mean and standard deviation , the ratio...Ch. 8 - Compute the measurement signal-to-noise ratio-that...Ch. 8 - Let Zn,n1, be a sequence of random variables and...Ch. 8 - Prob. 8.5TECh. 8 - Prob. 8.6TECh. 8 - Prob. 8.7TECh. 8 - Explain why a gamma random variable with...Ch. 8 - Prob. 8.9TECh. 8 - If X is a Poisson random variable with mean , show...Ch. 8 - Prob. 8.11TECh. 8 - Prob. 8.12TECh. 8 - Prob. 8.13TECh. 8 - Prob. 8.14TECh. 8 - The number of automobiles sold weekly at a certain...Ch. 8 - Prob. 8.2STPECh. 8 - If E[X]=75E[Y]=75Var(X)=10var(Y)=12cov(X,Y)=3 give...Ch. 8 - Prob. 8.4STPECh. 8 - Prob. 8.5STPECh. 8 - Prob. 8.6STPECh. 8 - Prob. 8.7STPECh. 8 - Prob. 8.8STPECh. 8 - Prob. 8.9STPECh. 8 - A tobacco company claims that the amount of...Ch. 8 - Prob. 8.11STPECh. 8 - Prob. 8.12STPECh. 8 - The strong law of large numbers states that with...Ch. 8 - Each new book donated to a library must be...
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- 8.1.12 Ishikawa et al. [“Evaluation of Adhesiveness of Acinetobacter sp. Tol 5 to Abiotic Surfaces,” Journal of Bioscience and Bioengineering (Vol. 113(6), pp. 719–725)] studied the adhesion of various biofilms to solid surfaces for possible use in environmental technologies. Adhesion assay is conducted by measuring absorbance at A590. Suppose that for the bacterial strain Acinetobacter, five measurements gave readings of 2.69, 5.76, 2.67, 1.62, and 4.12 dyne-cm2. Assume that the standard deviation is known to be 0.66 dyne-cm2. a. Find a 95% confidence interval for the mean adhesion. b. If the scientists want the confidence interval to be no wider than 0.55 dyne-cm2, how many observations should they take?arrow_forwardAnswer questions 8.2.1 and 8.2.2 respectivelyarrow_forward8.2.3 A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60,139.7 and 3645.94 kilometers. Find a 95% confidence interval on mean tire life. 8.2.4 Determine the t-percentile that is required to construct each of the following one-sided confidence intervals: a. Confidence level = 95%, degrees of freedom = 14 b. Confidence level = 99%, degrees of freedom = 19 c. Confidence level = 99.9%, degrees of freedom = 24arrow_forward
- 8.1.6The yield of a chemical process is being studied. From previous experience, yield is known to be normally distributed and σ = 3. The past 5 days of plant operation have resulted in the following percent yields: 91.6, 88.75, 90.8, 89.95, and 91.3. Find a 95% two-sided confidence interval on the true mean yield. 8.1.7 .A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ = 0.001 millimeters. A random sample of 15 rings has a mean diameter of x = 74.036 millimeters. a. Construct a 99% two-sided confidence interval on the mean piston ring diameter. b. Construct a 99% lower-confidence bound on the mean piston ring diameter. Compare the lower bound of this confi- dence interval with the one in part (a).arrow_forward8.1.2 .Consider the one-sided confidence interval expressions for a mean of a normal population. a. What value of zα would result in a 90% CI? b. What value of zα would result in a 95% CI? c. What value of zα would result in a 99% CI? 8.1.3 A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (38.02, 61.98) and (39.95, 60.05) a. What is the value of the sample mean? b. One of these intervals is a 95% CI and the other is a 90% CI. Which one is the 95% CI and why?arrow_forward8.1.4 . A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume that gain is normally distributed with standard deviation σ = 20. a. How large must n be if the length of the 95% CI is to be 40? b. How large must n be if the length of the 99% CI is to be 40? 8.1.5 Suppose that n = 100 random samples of water from a freshwater lake were taken and the calcium concentration (milligrams per liter) measured. A 95% CI on the mean calcium concentration is 0.49 g μ g 0.82. a. Would a 99% CI calculated from the same sample data be longer or shorter? b. Consider the following statement: There is a 95% chance that μ is between 0.49 and 0.82. Is this statement correct? Explain your answer. c. Consider the following statement: If n = 100 random samples of water from the lake were taken and the 95% CI on μ computed, and this process were repeated 1000 times, 950 of the CIs would contain the true value of μ. Is this statement correct? Explain your answerarrow_forward
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