Let a continuous random variable X denote the diameter of a hole drilled in a sheet of metal component. The target diameter is 12.5 mm. Most random disturbances to the process result in larger diameters. Historical data show that the distribution of X can be modeled by a pdf f(x)=20e-20(x-12.5), for x≥12.5. If a component with a diameter greater than 12.60 mm is scrapped. a) What portion of parts is scrapped? b) What portion of parts is between 12.5 and 12.6 mm? c) What is the mean and variance of X?

Suppose that the time-to-failure of a system has a distribution with the following pdf: f(x) = 0.1e^(-0.1x) What is the probability that the failure occurs between 5 and 20? a). 0.23 b). 0.47 c). 0.088 d). 0

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Clinical research attempts to identify the risks of exposure tothe population in the workplace. In a group of 46 menBetween the ages of 25 and 36, changes in the function of their lungs have been measured. One of the variables of interest was the volumeexhalation force (VFE), which is the volume of air exhaled per second. At the end of a certain period, it was found that the VFE of `this sample decreased with an average of 0.27 liters and a deviation0.52 liter sample type. We know that the VFE increases by 0.1liter in healthy men of the same ageduring the same period of time. Can we conclude that the middle ofwork of this group plays a significant role in the growth ofVFE greater than 0.1 liter? Choose the appropriate hypothesis testto do. Give the value - P and your conclusion. Take α = 0.02.

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The Elo Chess Rating System is a method for predicting scores from a chess match (in this case under a certain scenario). The probability of getting a certain score (for any real number x) is f(x)=(e^-(x-1000)/300)/(1+e^-(x-1000)/300)     The cumulative distribution function (for any real number x) is F(x)=1/(1+e^-(x-1000)/300)     What is the probability of getting a score of 699?Use 4 decimal placesWhat is the probability of getting a score less than 699?Use 4 decimal placesWhat is the probability of getting a score greater than 1509?Use 4 decimal placesWhat is the probability of getting a score between 699 and 1509?Use 4 decimal places

Question * Given X be the life time of a bulb having a probability density function f(x) =-e for x>0 and 0 elsewhere. The mean life time of the bulbs is equal to: %3D O 1/2 O None of these O 1/4 Question* Let X and Y be two independent continuous random variables with marginal distribution

Blood pressure Diastolic blood pressure in adults is normally |distributed with µ = 80 mm Hg and o = 12 mm Hg. In a ran- dom sample of 300 adults, how many would be expected to have a diastolic blood pressure below 70 mm Hg?

For the continuous probability function f(x ) = kx^2e^-x when 0≤x≤1. Find (a)k (b)mean (c)variance

The distribution of scores of students heading to college in the math section of the SAT follows a normal distribution with mean u = 520 and standard deviationo = 115. X = The score of a student heading to college in the math section of the SAT X = The mean score of 100 students heading to college in the math section of the SAT EX = The total score of 100 students heading to college in the math section of the SAT (Please show all formulas, calculations and the curves) (a) What math SAT score is 2 standard deviations below the mean? (b) What is the probability that the score of a student is less than 480? (c) What is the distribution of X? (d) What is the probability that the mean scores of 100 students is between 518 and 530? (e) What is the distribution of EX? (1) What is the probability that the total scores of 100 students is more than 51500? (g) What is the 65th percentile for the mean scores of 100 students?