7. The substrate concentration X (in mg/cm³) of effluent on a biofilm waste reactor is normally distributed, X~N(0.30,0.06). a) What is the probability that the concentration exceeds 0.50? b) 5% of all concentrations exceed what value?

Porosity measurements for several reservoir formations have been accomplished. The results imply that probability density function of the measurements is constant at a value of o.25. The used measurements in this study have porosity values from 4% to 8%. Determine the proportion of the measurements thathave 7%-8% porosity.

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Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma.

In a certain experiment, the error made in determining the density of a substance is evenly distributed between -0.0015 and 0.0015. Find the probability that such an error will exceed 0.0005 in absolute value. 11.

An insurer's annual weather related loss, X, is a random variable with density function   f(x) = 2.5 (200)2.5 / x3.5 for x >= 200 and 0 otherwise.   Calculate the 30th percentiles of X. (Round to 2 decimals).

When d.f. É31:to.00s=2.74, to.a=2.453,toors=2.040, fritical Valuusiza.c5=257520.0=2.325,z0.025=1 2.025=1,916, Z0.05=1.1d5,Z0.1= lv282 en d.f. 31:t0.005=2.44.t0.9=2.463.to025=2.OLIO, %3D %3D %3D to.os=\.l6916, to.1=\.309 Lin a random ht in the Battle of Preston, 77 New Model Amy, and e Royalist Army. Aest the claim that fever than one quarter of the soldiers were Rayaliste, sample of soldiers who fou soldiers were from the 2266 were from the . Use a 0.05 significance level to

Defects occur along the length of cable at an average of 5 defects per 4,000 feet. Assume that the probability of k defects in t feet of cable is given by the probability mass function: -( 5t/ 4000) '(5t/4,000)k e P(k defects ) = k! for k = 0, 1, 2, .. Find the probability that a 3,200 foot cable will have a. at most three defects b. at least four defects C. between 1 to 5 (inclusive) defects

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.50 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit     1 upper limit     2 margin of error     3 (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of weights is normal σ is known the distribution of weights is uniform σ is unknown (c) Interpret your results in the context of this problem. 1% of the intervals created using…

Porphyrin is a pigment in blood and other body fluids that is significant in body energy and storage.  Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood.  In healthy adults x is approximately normally distributed with μ = 38 and σ = 12.  What is the probability that x is less than 60?