50 soil samples from a contruction site were tested for shear strength. The mean of the samples was determined to be 4270kN/m^2. The standard deviation was estimated to be 553kN/m^2. Assuming the data are normally distributed, what is the minimum shear stregnth that can be used for design if we accept a risk that 1% of test sample will fall bellow that minimum strength?
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50 soil samples from a contruction site were tested for shear strength. The mean of the samples was determined to be 4270kN/m^2. The standard deviation was estimated to be 553kN/m^2. Assuming the data are
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- The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 4 mm and a standard deviation of 0.03 mm. Suppose that the process will be monitored by selecting a random sample of 25 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 25. The distribution of x is ---Select-- ✓with mean 4- 20x = 4 + 20 = (b) When no unusual circumstances are present, we expect x to be within 20 of 4 mm, the desired value. An x value farther from 4 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 4 ± 20x mm mm and standard deviation mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 4 ± 20 just by chance (that is, when there…Someone once dropped a 'mint imperial", a type of sweet, from the top of a multi-story car park and it landed on my grandmother's head. The average speed of a falling mint imperial is 4 m/s and the velocity is a Gaussian distribution with standard deviation 0.25 m/s. If a mint travelling faster than 5 m/s causes injury, what is the chance my grandmother was injured? In fact she was fine, but very annoyed. O(i- erf (2/2)/2 O [1- erf (v2)/2 O [1- erf (2) O [1- erf (4)/2The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of X is ---Select--- ✓with mean mm and standard deviation mm mm mm. (b) When no unusual circumstances are present, we expect x to be within 20 of 3 mm, the desired value. An x value farther from 3 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 3 ± 20%. 3 - 20- 3 + 20 = (c) Referring to part (b), what is the probability that a sample mean will be outside 3 ± 20-just by chance (that is, when there…