Kindly answer it 1. A shipping company handles containers in three different sizes: (1)27 ft³ (3 × 3 × 3), (2) 125 ft³ and (3) 512 ft3. Let Xi (i = 1,2,3)denote the number of type i containers shipped during a given week.With E(X) and σ = var(X₁), suppose that the mean values andstandard deviations are as follows:fi=με=200, 2250, μз 10001 10,02 12, 03 = 8.==(a) Assuming that X1, X2, X3 are independent, calculate the expectedvalue and variance of the total volume shipped. [Hint: Volume=27X1+125X2 + 512X3.](b) Would your calculations necessarily be correct if the X's were notindependent? Explain.

Detailed Solution for Expected Value and Variance of Total Volume Shipped:1. Defining Variables:•…

Answered: 1. A shipping company handles…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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The variable X, is the carbon monoxide concentration in air, and ten measurements are obtained as follows: 10.25, 10.37, 10.66, 10.47, 10.56, 10.22, 10.44, 10.38, 10.63, 10.40 mg/m3 . (i) Test whether the mean concentration of carbon monoxide in air is 10.00 mg/m3 . (ii) Calculate the power of the above test if the mean concentration of carbon monoxide in the alternative hypothesis is assumed to be 10.75mg/m3 .
Suppose u, and µ, 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 = 7, x = 113.3, s, = 5.02, n = 7, y = 129.8, and s, = 5.32. 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.) n USE SALT |-22.52 |-10.48 Does the interval suggest that precise information about the value of this difference is available? O Because the interval is so wide, it appears that precise information is available. O Because the interval is so narrow, it appears that precise information is not available. O Because the interval is so wide, it appears that precise information is not available. O Because the interval is so narrow, it appears that precise information is available.
Suppose u, and u, 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 = 5, x = 115.1, s, = 5.05, n = 5, y = 129.2, and s, = 5.36. 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.) n USE SALT Does the interval suggest that precise information about the value of this difference is available? O Because the interval is so narrow, it appears that precise information is available. o Because the interval is so wide, it appears that precise information is not available. o 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. You may need to use the appropriate table in the Appendix of Tables to answer this question.
Suppose u, and µ, 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 = 7, x = 113.3, s. = 5.02, n = 7, y = 129.8, and S2 = 5.32. 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.) In USE SALT Does the interval suggest that precise information about the value of this difference is available? Because the interval is so wide, 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 not available. Because the interval is so narrow, it appears that precise information is available.
A shipping company handles containers in three different sizes: (1) 27 ft³ (3 × 3 × 3), (2) 125 ft³, and (3) 512 ft³. Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With μ; = E(X;) and 0,2² = V(X), suppose that the mean values and standard deviations are as follows: = = 220 M1 01 10 M2 02 = = 250 = 13 μ3 = 03 = = 150 = 6 (a) Assuming that X1, X2, X3 are independent, calculate the expected value and variance of the total volume shipped. [Hint: Volume = 27X₁ + 125X2 + 512X3.] expected value variance ft³ ft6 1 (b) Would your calculations necessarily be correct if the X,'s were not independent? Explain. The expected value would be correct, but the variance would not be correct. The expected value would not be correct, but the variance would be correct. Neither the expected value nor the variance would be correct. Both the expected value and the variance would be correct.
la). The null hypothesis is that the difference in the grams of sugar between ultra-processed and processed food μ = 0 (Ho: μ = 0). Write an example alternative hypothesis for the mean (µ) difference between ultra-processed foods (up) and processed foods (μ). 1b). Next, generate 1,000 samples. Let's say that you asked students in our class to calculate the difference in the amount of sugar between their ultra-processed food and processed food at home, which had a mean (u) sugar difference of 14.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1c). Let's say that your sample difference in the amount of sugar between ultra-processed food and processed food at home was 4.75 grams of sugar. Do you have evidence to reject the null hypothesis? 1d). What is a 92% confidence interval for the data? Please write it using the full confidence interval interpretation language (e.g., I am 92% confident that...). le). What percent of the data lie to the left of -14.25 grams of…
please solve a and b.
Assume that the length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean μ=266μ=266days and σ=16σ=16 days (in other words, X∼N(266,16)X∼N(266,16). Use a calculator or Excel to find the following values. a. What pregnancy length is less than 50% of the other pregnancy lengths? b. What length of pregnancy is shorter than 97.5% of all pregnancy lengths? Use 4 decimal places. c.Between what two numbers do the middle 70% of all pregnancy lengths fall? Use 4 decimal places.
I need help with these two questions. Here are the data table if needed. The absolute viscosity for sunflower oil is supposed to average 0.0311 Pa⋅s at 38 ∘C. Suppose a food scientist collects a random sample of 4 quantities of sunflower oil and computes the mean viscosity for his sample to be x¯=0.0318 Pa⋅s at 38 ∘C. Assume that measurement errors are normally distributed and that the population standard deviation of sunflower oil viscosity is known to be σ=0.0009 Pa⋅s. The scientist will use a one‑sample z‑test for a mean, at a significance level of α=0.01, to evaluate the null hypothesis, H0:μ=0.0311 Pa⋅s against the alternative hypothesis, H1:μ≠0.0311 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample z‑statistic, the p‑value, and then deciding whether to reject the null hypothesis. First, compute the z‑statistic, z. Provide your answer precise to two decimal places. Avoid rounding within calculations. z= Determine the…
The weight of a carton of a dozen eggs produced by a certain breed of hens is supposed to be normally distributed with a mean of 780 grams. A quality manager randomly checks thirty-five cartons of eggs (n = 35) to see whether the mean weight differs from 780 grams. She finds x̄ = 796. 1. What is the parameter of interest? The mean weight of 35 cartons of eggs produced by a certain breed of hens The mean weight of all cartons of eggs produced by a certain breed of hens The weight of all cartons of eggs produced by a certain breed of hens The mean weight of all eggs produced by a certain breed of hens 2.What are the null and alternative hypotheses? H 0: μ = 780 vs. H a: μ ≠ 780 H 0: μ = 780 vs. H a:μ < 780 H 0: μ = 780 vs. H a: μ > 780 H 0: x̄ = 780 vs. H a: x̄ ≠ 780
The following scatterplot shows the mean annual carbon dioxide (CO,) in parts (CO2) per million (ppm) measured at the top of a mountain and the mean annual air temperature over both land and sea across the globe, in degrees Celsius (C). Complete parts a through h on the right. f) View the accompanying scatterplot of the residuals vs. CO2. Does the scatterplot of the residuals vs. CO, show evidence of the violation of any assumptions behind the regression? 16.800 A. Yes, the outlier condition is violated. 16.725 O B. Yes, the linearity and equal variance assumptions are violated. 16.650 C. Yes, the equal variance assumption is violated. 16.575 O D. No, all assumptioris are okay. 16.500 O E. Yes, all the assumptions are violated. 325.0 337.5 350.0 362.5 CO2 (ppm) OF Yes, the linearity assumption is violated. his vear, What mean temperature does
A variable of two populations has a mean of 55 and a standard deviation of 24 for one of the populations and a mean of 55 and a standard deviation of 40 for the other population. Complete parts (a) through (c) a. For independent samples of size 16 and 25, respectively, find the mean and standard deviation of x1 - x2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x, - x, is (Type an integer or a decimal. Do not round.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Explain your answer. c. Can you conclude that the variable x, - x, is normally distributed? Explain your answer.

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