Penicillin is produced by the Penicillium fungus, which is grown in a broth whosesugar content must be carefully controlled. The optimum sugar concentration is 4.9mg/mL. If the concentration exceeds 6.0 mg/mL, the fungus dies and the process mustbe shut down for the day.2If sugar concentration in batches of broth is normally distributed with mean 4.9mg/mL and standard deviation 0.6 mg/mL, examine the proportion of days theprocess must be shut down.(a)The supplier offers to sell broth with a sugar content that is normally distributedwith mean 5.2 mg/mL and standard deviation 0.4 mg/mL. Evaluate the broth.(b)

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Answered: Penicillin is produced by the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when u = 1680 cycles.
The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. Ho: u = 5.5 Hg: µ 2 5.5 Ho: H = 5.5 HaiH 5.5 = Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the…
In a manufacturing industry, the amounts which go into raw materials (Scraps) are supposed to be normally distributed with mean GHC 36. and standard deviation GHC 0.1. Once every 30 minutes a scrap is selected from the production line, and its contents are noted precisely. If the amount of the scrap goes below GHC 35.8. or above GHC 36.2, then the scrap will be declared out of control. i)If the process shifts so that μ = GHC 37 and σ = GHC 0.4, find the probability that a scrap will be declared out of control
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.
Show step by step 1 Simulate the failure times of 100 units randomly selected from a Weibull distributionwith characteristic life θ = 100 and shape parameter α = 3. Plot the histogram ofthese 100 data points and comment on this histogram. 2. Suppose the data of the last question came from a life testing but the test was stoppedat the 50-th failure. Re-organize the data set and re-plot the histogram. Compare thisplot with the previous plot and comment on these plots. Show step by step
A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 215 225 235 240 255 260 225 Total Blood Cholesterol (After) 214 222 240 237 254 257 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μd=μ1−μ2. Choose the correct…
The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…
Can you assist me in answering this? I do not receive results, and it would be helpful to know if I am on the right track to study for midterms. (this is not graded but, rather, an excersice conducive to acquisition).
Albumin is a liver protein that helps circulate vitamins throughout the body. Reduced Albumin has been associated with severe illness with Covid-19 patients. Suppose we wanted to conduct a study to compare the mean Albumin concentration (g/L) between a sample of adult patients hospitalized for Covid 19 (Sample Mean= 32.8, s=6.0) to the mean albumin concentration (g/L) of healthy adults (u=34.1, o=7.13). How many patients would need to enroll from the hospital to conduct this study with 99% confidence, and 80% power? A. 267 B. 120 C. 352 D. 225
Researchers analyze a new portable radiocarbon dating machine and determine that the machine will correctly predict the age of an archaeological object within established tolerances 70% of the time. The machine's inventor wants to test this claim, believing that her machine correctly predicts age at a greater rate. Let p represent the proportion of times that the new portable radiocarbon dating machine correctly determines the age of an archaeological object to within the established tolerances. The inventor's null and alternative hypotheses are as follows. Но : р 0.70 На : р> 0.70 The inventor takes a random sample of n = 100 archaeological objects for which the age is already known and uses her machine to determine the age of each object. The machine correctly determines the age of 78 of the objects in the sample. What is the value of the standardized test statistic? (Round to 2 decimal places)

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