Showing 241 to 250 of 287 Questions
  • The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) =e-x/100/1000 for x > 0 Determine the probability that(a) A component lasts more than 3000 hours before failure.(b) A component fails in the interval from 1000 to 2000 hours.(c) A component fails before 1000 hours.(d) Determin

  • The probability distribution of A, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by Construct the cumulative distribution function ofX.

  • The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function(a) Show that P(0 < X < 1) = 1.(b) Find the probability that more than 1/4 but fewer than 1/2 of the people contacted will respond to this type ofsolicitation.

  • The proportion of the budgets for a certain type of industrial company that is allotted to environmental and pollution control is coming under scrutiny. A data collection project determines that the distribution of these proportions is given by(a) Verify that the above is a valid density.(b) What is the probability that a company chosen a

  • The random variables X and Y, representing the weights of creams and toffees in 1-kilogram boxes of chocolates containing a mixture of creams, toffees, and cordials, have the joint density function(a) Find the probability density function of the random variable Z = X + Y.(b) Using the density function of Z, find the probability that in a

  • The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds.(a) What is the probability that a reaction requires more than 0.5 seconds?(b) What is the probability that a reaction requires between 0.4 and 0.5 seconds?(c) What is the reaction time that is excee

  • The shelf life of a product is a random variable that is related to consumer acceptance. It turns out that the shelf life Y in days of a certain type of bakery product has a density function what fraction of the loaves of this product, stocked today would you expect to be sellable 3 days from now?

  • The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function Find the probability that a bottle of this medicine will have a shell life of(a) At least 200 days;(b) Anywhere from 80 to 120days.

  • The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours.(a) What is the probability that the sick-leave time for next month will be between 50 and 80 hours?(b) How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a

  • The speed of a file transfer from a server on campus to a personal computer at a student’s home on a weekday evening is normally distributed with a mean of 60 kilobits per second and a standard deviation of 4 kilobits per second.(a) What is the probability that the file will transfer at a speed of 70 kilobits per second or more?(b) What

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