3. a). Let X be normal with mean 50 and variance 9. Determine c such that P (X< c) = 5%,P (X> c) =1 %, P (50 – c

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Answered: 3. a). Let X be normal with mean 50 and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
5. Suppose that f: R → R is a continuously differentiable function (of class C¹) and that there is a positive number c> 0 such that f'(x) > c Vx ER Prove that f(x) ≥ ƒ(0) + cx Prove that f is surjective. That is, ƒ(R) = R. Prove that f is a diffeomorphism from R onto R. That is, f-¹ exists and is differentiable. (Hint: One can consider Mean Value Theorem, Intermediate Value Theorem and Inverse Function Theorem.) if x ≥ 0 and f(x) ≤ f(0) + cx if x ≤ 0
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.
Assume that IQ scores are normally distributed with μ = 100 and σ = 15 What IQ score would be needed to score in the top 2% of IQ scores?
3.1. Suppose that the height of the women is a normal variable with a mean of 1.62 meters (m) and a standard deviation of 24 centimeters. Calculate the percentage of women who measures (a) more than 1.70 m. (b) between 1.66 and 1.58 m. (c) less than 1.50 m. d) between 1.60 and 1.63 m.
3. Suppose that X has an exponential distribution with a mean of 10. Determine the following: (a) P(X 15) (c) Compare the results in parts (a) and (b) and comment on the role of memoryless property.
13. Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.31 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.37 parts per million and the standard deviation is 2.12 parts per million. At α=0.10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Which of the following correctly states H0 and Ha? H0: muμ greater than or equals≥ 2.31 2.31 Ha: muμ less than< 2.31 2.31 (Type integers or decimals. Do not round.) The claim is the alternative hypothesis. Part 2 (b) Use technology to find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t0=negative 1.30 −1.30. (Use a comma to separate answers as…
18. A set of n = 52 pairs of scores (X and Y values) in a research study has a Pearson correlation of r = -0.7. What percentage of the variance for the Y scores is predicted by its relationship with X?
12. The following means, standard deviations and correlations are found for X1 = = seed hay crop in cwts. per acre, X2 = spring rainfall in inches, X3 = accumulated temperature above 42° F in spring, in a certain district of England during twenty years. %3D |3D X = 28-02, 01=4-42, r12 =+ 0-80, 0.40, X2 = 4.91, 02 = 1·10, r13 =- -- Ò -56. %3D X3 = 594, ơ3 = 85, r23 = - 0-56. %3D Find the partial correlations and the regression equations for hay-crop on spring rainfall and accumulated temperature,
The expectation of X, which is also known as the mean or average, is E(X) = 7 and the Variance of X is var(X) =4. Using the equation Y = 11X + 81. What are the expected value E(Y), variance VAR(Y), and standard deviation SD(Y) of this expression.
Suppose ₁ and ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 9, x = 113.3, s₁=5.01, n = 9, y = 129.6, and s₂ = 5.34. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) USE SALT -21.57 1x ) Does the interval suggest that precise information about the value of this difference is available? Because the interval is so narrow, it appears that precise information is available. Because the interval is so narrow, it appears that precise information is not available. Because the interval is so wide, it appears that precise information is available. Because the interval is so wide, it appears that precise information is not available. x -11.06

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3. a). Let X be normal with mean 50 and variance 9. Determine c such that P (X c) =1 %, P (50 – c