Seventy percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive vehicles pass or fail independently of one another, calculate the following probabilities. (Enter your answers to three decimal places. (a) P(all of the next three vehicles inspected pass) 0.512 x (b) P(at least one of the next three inspected fails) 0.063 x

In the table below x denotes the X-Tract Company’s projected annual profit (in $1,000).  The table also shows the probability of earning that profit.  The negative value indicates a loss.   x f(x)   x = profit   -100 0.01   f(x) = probability -200 0.04       0         100 0.26       200 0.54       300 0.05       400 0.02         12 If we add $45 to each value in the profit/loss column above, the new variance of profit will be,   a 12,169               b 11,741               c 11,696               d 11,467

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X P(x) =C p*q"-x %3D When processing credit-card applications there is a 40% chance that an application will have incomplete or insufficient information and require research. You have 5 applications in your to-do pile and would like to leave early today. (a) Fill in the values: n = q = (b) What is the probability of exactly three applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= (c) What is the expected number of applications that will need research? Answer= (d) What is the probability of having AT LEAST the expected number of applications needing research? (enter a number between 0 and 1, 4 decimal places) Answer= Please answer all parts of the question.