A certain mechanical component is to be manufactured with a diameter of 3 centime-ters. The manufacturing process produces components whose diameters are normallydistributed with mean value = 3 and standard deviation is 0.02 cm.(a) What percentage of components will have a diameter greater than 3.045 cm?(b) What percentage of components with have a diameter less than 2.95 cm?(c) If the manufacturer discards any component with a diameter that differs from 3 cmby more than 0.03 cm (in either direction), then what percentage of componentswill be discarded?

Introduction: Denote X as the diameter of a randomly selected component. It is given that X has a…

Answered: A certain mechanical component is to be…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The engineer of large manufacturing company takes many measurements of a specific dimension of components from the production line. She finds that the distribution of dimensions is approximately normal, with a mean of 3.33 cm and a coefficient of variation of 3.60%. i. What percentage of measurements will be less than 3.50 cm? What percentage of dimensions will be between 3.10 cm and 3.50 cm? What percentage of measurements will be equal to 3.50 cm? What value of the dimension will be exceeded by 90% of the components? ii. iii. iv.
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.
High density lipoprotein (HDL) in healthy males follows a normal distribution with a mean of 50 and a standard deviation of 8. What proportion of healthy males has HDL exceeding 60?
A distribution with µ = 55 and o = 6 is being standardized so that the new mean and standard deviation will be u = 50 and o = 10. When the distribution is standardized, what value will be obtained for a score of X= 58 from the original distribution?
The finished inside diameter of a piston ring is normally distributed with a mean of 10 cm and a standard deviation of 0.03 cm. Below what value of inside diameter will 15% of the piston rings fall?
The measurement of the distance to a certain object is accompanied by systematic and random errors. The systematic error equals 50 m. in the direction of decreasing distance. The random errors obey the normal distribution law with the mean-square deviation = 100 m. Find (1) the probability of measuring the distance with an error not exceeding 150 m. in absolute value, (2) the probability that the measured distance does not exceed the actual one.
Steel rods are manufactured with a mean length of 26centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.05 cm. Complete parts (a) to (d). (a) What proportion of rods has a length less than 25.9cm?
2. Suppose the chamber of commerce at Pyramid Lake advertises that the average length of trout caught at the lake is μ = 19 inches. However, a fishing magazine survey reported that for a random sample of 51 fish caught, the mean length was x = 18.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of the trout caught at Pyramid Lake is less than μ = 10 inches? (Use α = 0.05)
= 222 mg/dLi and Total cholesterol levels for middle aged men (aged 55 – 64) follow approximately a normal distribution with mean, µ standard deviation, o = 37 mg/dLi. Those with a total cholesterol of 240 mg/dLi or higher have "high" cholesterol (and have twice the risk of coronary heart disease as someone with a total cholesterol less than 200 mg/dLi) Find the Z-score (standard score) for an observation of 290 mg/dl.
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.
The weight, in grams, of red beans in a can is normally distributed with mean u and standard deviation 7.6. Given that 5% of cans contains less than 200g, determine; (b) (i) The value of u. (ii) The percentage of cans that contains more than 225 g of beans.
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)?

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