X P(X) X · P(X) (х — и)2 (X – µ)² · P(X) 0.05 10 0.34 15 0.26 20 0.25 25 0.10
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Find the mean, variance, and standard deviation of the following probability distribution by completing the tables below.
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- Cesium-137 has a half-life of about 30 years. If we begin with 200 mg of cesium-137, will it take more or less than 230 years until only 1 milligram remains?Solve for x: z=x.Suppose the proportion of all college students who have used marijuana in the past 6 months is p=0.40.ln a class of 150 students that are representative of all college students,would it be unusual for the proportion who have used marijuana in the past 6 months to be less than 0.33? Yes No Cannot be determined. Explain how you made your decision in the above question.
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- 5. The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t . After 3 hours it is observed that 400 bacteria are present. After 10 hours 2000 bacteria are present. What was the initial number of bacteria?15. As x increases uniformly at the rate of 0.002 feet per second, at what rate is the expression (1 + x) to the 3rd power increasing when x becomes 8 feet?A radioactive material is known to decay at the rate proportional to the amount present. If initially there is 50 mg of the material and after 2 hours, it is observed that the material has lost 10% of its original mass.a. Find the expression for the approximate amount of radioactive material present at any time t.b. Determine the mass of the material after 4 hours.c. Determine the half-life of the material.
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