Statistics and Probability Answers

Customers arrive at a checkout counter in a department store according to a Poison distribution of an average of seven per hour.During a given hour,what are the probabilities that

(a).no more than three customers arrive?

(b).at least two customers arrive?

(c).exactly four customers arrive?

A missile protection system consist of "n" radar sets operation independently,each with a probability of .9 of detecting a missile entering a zone that is covered by all the units.

(a).If "n"=5 and a missile enters the zone,what is the probability that exactly four sets detect the missile?At least one set?

(b).How large must "n" be if we require that the probability of detecting a missile that enters the zone be .999?

A complex electronic system is built with a certain number of buckup components in its subsystems.One subsystem has four identical components,each with a probability of 2 of failing in less than 1000 hours.The subsystem will operate if any two of the four components are operation.Assume that the components operate independently.Find the probability that;

(a).Exactly two of the four components last longer than 1000 hours.

(b).The subsystem operates longer than 1000 hours.

A multiple-choice examination has 15 questions,each with five possible answers,only one of which is correct.Suppose that one of the students who takes the examination answers each of the questions with an independent random guess.What is the probability that he answers at least ten questions correctly?

Let the "pdf" of X be given by "f(x)=0.25exp(-0.25x),x>0"

Show that "E(X)" =4 and "Var(X)" =16.

Suppose Y is a random variable with pdf f(y)=ay²-b,0<y<3

Find a and b given that E(Y)=15/7

Data shows that 25% of treadmills at a gym have errors in their electronics. A technician randomly selects six treadmills.

10.

The probability that four of these treadmills have errors in their electronics is:

On a research it was found that 47% of residents travelers were women and 53% men. A random sample of 500 travelers on a large airline revealed that of those 500, 263 were women. Using a=0.05 compute CV, and TV, and state the hypotheses and your conclusion.

The data shows the number of students attending a private school in the city and the number of students attended schools in the suburb. At a=.01, is there enough evidence to support the claim that the average number of students attending a private school in the city is greater than the number of students attending the suburb schools?

private school

25 75 38 41 27 32  

suburbs

57 25 38 14 10 29

On a research it was found that 47% of residents travelers were women and 53% men. A random sample of 500 travelers on a large airline revealed that of those 500, 263 were women. Using a=0.05 compute CV, and TV, and state the hypotheses and your conclusion.