**5.2.4 Probability and Product Specifications**A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03 grams. Any lamp with less than 1.14 grams of luminescent ink fails to meet customers’ specifications. A random sample of 25 lamps is collected, and the mass of luminescent ink on each is measured.**Questions:****a.** What is the probability that at least one lamp fails to meet specifications?**b.** What is the probability that five or fewer lamps fail to meet specifications?**c.** What is the probability that all lamps conform to specifications?**d.** Why is the joint probability distribution of the 25 lamps not needed to answer the previous questions?

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Answered: 5.2.4 WP A manufacturer of…

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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8. 140 migrating pigeons were caught by a biologist for data collection. The mass of these pigeons is normally distributed with mean 0.9 kg and standard deviation of deviation 0.15 kg. a) Determine the percentile rank of a pigeon weighing 1kg. b) What proportions of pigeons have weight greater than 1.1 kg or less than 0.7 Kg 31
The blood pressure (average of systolic and diastolic measurements) of each of 25 randomly selected persons was measured. The average was 97.5 mm Hg, and the standard deviation was 8.05 mm Hg. What is the critical t value? What is the margin of error?
The time it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.9 seconds and standard deviation 4.1 seconds. Find and interpret the z-score for x = 26.4.
Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 306.03 newtons and 41.95 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Round your answers to three decimal places.) n USE SALT
An engineer working for a tire manufacturer investigates the average life of a new material to be used in the manufacturing process. For this purpose, he builds a sample of 13 tires and tests them in a laboratory until the end of their useful life is reached. The data obtained from the sample are as follows: average of 60897.9 km and standard deviation of 2734.8 km. The engineer would like to demonstrate that the average service life of the tire with the new material exceeds 60,000 km. a) State the null and alternative hypothesis to be stated in this experiment. Test the stated hypotheses using an α = 0.05 What conclusions are reached? b) Find a 95% confidence interval for the average tire life with the new material. Interpret your answer. (RESPOND MANUALLY) (RESPOND MANUALLY)
Listed in the data table are amounts of strontium-90 (in millibrcquerels or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. Find the test statistic, p value, and confidence interval
(3) A process for manufacturing soft soda produces normally distributed yield with a mean of 600 and a standard deviation of 100 units. A new modified process yields an average of 630 units for a sample of size 50. At a = 0.05 does the modified process increase the yield? %3D
3) A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times, with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With a substrate concentration of 2.0 moles per liter, 12 runs were made, yielding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances
Currently patrons at the library speak at an average of 61 decibels. Will this average increase after the installation of a new computer plug in station? After the plug in station was built, the librarian randomly recorded 57 people speaking at the library. Their average decibel level was 63.8 and their standard deviation was 9. What can be concluded at the the αα = 0.10 level of significance?
O C. The baby born in week 41 weighs relatively less since its z-score, is larger than the z-score of for the baby born in week 32. O D. The baby born in week 32 weighs relatively less since its z-score, is smaller than the z-score of for the baby born in week 41.
In a study of microplastics in our environment, it was determined that there are 5.25 trillion plastic pieces floating in the ocean, weighing more than 250,000 tons. In a recent expedition to examine whether increases in plastic production have led to changes in ocean microplastics, 16 samples were taken at various locations in the Pacific Ocean. It was determined that the average concentration was 9.5 particles per liter of ocean water with a sample standard deviation of 6. In one of the earliest research expeditions to study microplastics in the ocean conducted in 2009, it was determined that the average concentration of microplastics was 6 particles per liter (consider this the population or reference mean). What is the critical value for the two-tailed alternative hypothesis at alpha = 5%? (Hint: This is the value in the table that you will compare your test statistic to in order to determine the outcome of the hypothesis test). 2.131 1.746 2.120 1.753
Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens under specified conditions, and the resulting mean and standard deviation were 306.11 newtons and 41.94 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.) n USE SALT

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