1) The laser offset is known to have a normal distribution with population mean of 100 nm and population standard deviation of 2 nm. i) What proportion of the laser offset will be between 99.5 nm and 103.0 nm?
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- Suppose that replacement times for washing machines are normally distributed with a mean of μ=8.7 years and a standard deviation of σ=1.6 years. Find P25 the replacement time that separates the bottom 25% from the top 75%Spray drift is a constant concern for pesticide applicators and agricultural producers. The inverse relationship between droplet size and drift potential is well known. The paper "Effects of 2,4-D Formulation and Quinclorac on Spray Droplet Size and Deposition"+ investigated the effects of herbicide formulation on spray atomization. A figure in a paper suggested the normal distribution with mean 1050 µm and standard deviation 150 µm was a reasonable model for droplet size for water (the "control treatment") sprayed through a 760 ml/min nozzle. USE SALT (a) What is the probability that the size of a single droplet is less than 1380 µm? At least 950 µm? (Round your answers to four decimal places.) less than 1380 μm at least 950 μm (b) What is the probability that the size of a single droplet is between 950 and 1380 µm? (Round your answer to four decimal places.) (c) How would you characterize the smallest 2% of all droplets? (Round your answer to two decimal places.) The smallest 2% of…Emissions of sulfur dioxide set off chemical changes in the atmosphere that result in "acid rain." The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose the pH of rain at one location varies among rainy days according to a Normal distribution with mean 5.30 and standard deviation 0.43. What proportion of rainy days have rainfall with pH below 5.0?
- For each substance, estimate the standard deviation o by assuming uniform distribution and normal distribution shown in Table 8.11 in Section 8.8. (Round your answers to 4 decimal places.) Uniform Distribution Normal Distribution Chromium Barium FluorideA survey collected data from a random sample of 121 people living in Jade city. The sample average of the distance people travel to reach their workplaces (Y) is 23.28 km and the standard deviation (sy) is 7.48 km. The standard error of the sample average of the distance people travel to reach their workplaces is 68 km. (Round your answer to two decimal places.) Let μy denote the mean of the distance all the people in Jade city travel to reach their workplaces. The p-value of the test Ho: #y #22 km vs. H₁: Hy #22 km is (Round your answer to two decimal places.)The boiling point of 16 samples of a certain brand of hydrogenated vegetable oil used in a fryer was collected, resulting in Xbar=152.1 degrees. Assume that the distribution of melting point is normal with o=3.20. If the boiling point is different than 150 degrees, then either the oil will be too hot and will burn food or it will be too cool and will not properly cook the food. Is the sample mean significantly different from the target of 150 degrees? Use alpha=0.01 Но: H1: Define critical (rejection) region(s): Calculate the appropriate test statistic: What decision do we make? What this decision means in terms of this problem?
- A person's body mass index (BMI) is computed by dividing the weight (kg) by the square of height (m). The accompanying table contains the BMI statistics for random samples of males and females. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Let population 1 be females. Female BMI: n=69 x=29.14 s=7.41 Male BMI: n=79 x=28.18 s=5.24 The test statistic is The P-value is Construct a confidence interval appropriate for testing the claim in part (a). The ___% confidence interval estimate is ___<μ1−μ2<___.The average height X and weight Y of males in population have a bivariate normal distribution with means µX 1.80 m., µy 90.0 kgs and standard deviations Ox = 0.30 m., oy = 15.3 kgs respectively. The correlation coefficient between X and Y is p= 0.80.The level of calcium in the blood of healthy young adults follows a normal distribution with mean u = 10 milligrams per deciliter and standard deviation s = 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The sample mean of these 100 measurements is X = 9.8. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this question, we perform the following hypothesis test: H0: u = 10, Ha: u < 10. What is the test statistic? (use two decimal places in your answer) What is the p-value equal to? At the 10% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT t the 5% significance level, do you accept or reject the null hypothesis? Answer ACCEPT or REJECT
- A certain variable has a bell-shaped distribution with mean μ=176.16μ=176.16 and standard deviation σ=4.9σ=4.9. You observe a value of x=184x=184. Is this a TYPICAL value of the variable (within 2 standard deviations of the mean), or an UNUSUAL one (more than 2 standard deviations from the mean)?A normal population has a mean μ = 31 and standard deviation = 8. What proportion of the population is less than 29?
