Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.4, Problem 44E
Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in Exercise 15 of Section 12.2 resulted in ŷ = 7.592, sŶ = .179 when x = 40 and ŷ = 9.741, sŶ = .253 for x = 60.
- a. Explain why sŶ is larger when x = 60 than when x = 40.
- b. Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40.
- c. Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40.
- d. If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?
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Microsoft Excel snapshot for random sampling: Also note the formula used for the last
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0.941323044
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0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
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WASHINGTON
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Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
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No.
States
Rand No. Random Sample
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Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined.
1.What percent of the refunds are more than $3,500?
2. What percent of the refunds are more than $3500 but less than $3579?
3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts?
1. Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the answer of the second part.)
2. Compute the probability of a value greater than 55.0.
Use the same formula, x=55 and subtract the answer from 1.
3. Compute the probability of a value between 52.0 and 55.0.
(The question requires finding probability value between 52 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 52, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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