The amount of impunity of a product is a rv with mean 4.0g and standard deviation 1.5g. If 50 batches are independently prepared, what is the distribution of average impunity X ? what is the probability that X is between 3.5g and 3.8g ? If we randomly select 100 products, what is the probability that the total of the impunity is at most 425g?
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- The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.6 and B = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.7520 0.7520 0.1065 x X X (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 0.6312 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) 191 XhrA machine produces small rods and large rods. The diameters of small rods are normally distributed with mean 2 cm and standard deviation 0.12 cm. The diameters of large rods are normally distributed with mean 2.2 cm and standard deviation 0.15 cm. (i) Find the probability that a randomly chosen small rod has diameter greater than 2.15 cm. (ii) A box contains one small rod and one large rod. Find the probability that at least one of the rods has diameter greater than 2.15 cm.
- (b) A company has 16 cars of this model in its fleet. What is the probability that the average NOX + NMOG level x¯ of these cars is above 90 mg/mi? - life for one car model vary Normally with mean 84 mg/mi and standard deviation 6 mg/miA certain brand of automobile tire has a life expectancy that is normally distributed with a mean of µ= 20000 miles and standard deviation of o= 2500miles. What is the probability that a randomly chosen tire will last for 20000 miles or more? Select one: a. 0.1047 O b. 0.5 O c. 0.1784 O d. 0.1064A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is more than 60?
- 5. Daily sales of a store is normally distributed with mean µ=180 Rials and variance o =100. Find the probability that total sales over a period of nine days is more than 1800 Rials. Z= p=A proton emitter produces proton beams with changing kinetic energy that is uniformly distributed between three and eight joules. Suppose that it is possible to adjust the upper limit of the kinetic energy (currently set to eight joules). • What is the mean kinetic energy? What is the variance of the kinetic energy? What is the probability that a proton beam has a kinetic energy of exactly 3.5 joules? a. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a continuous distribution O b. E(X) = 5, V(X) = 1.33, probability is zero (0) because X has a uniform distribution O c. NONE O d. E(X) = 5.5, V(X) = 2.0833, probability is zero (0) because X has a uniform distributionThe Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.4 and ß = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.) at most 250 less than 250 more than 300 0.74310 0.74310 0.12183 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) 6032 (c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.) hr