Binomial Distribution Case Study

a) In a binomial experiment if p(x=0) =0.0041 and p(x=1) =0.041 are the result of 5 trials then find the value of p and q.

b) Write any three properties of binomial distribution.

c) Three cards are chosen at random from a deck of 52 playing cards without replacement. What is the probability of getting a jack, a ten and a nine in order?

d) A city survey found that 45% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job given that he plans to attend college?

e) Each of 10 computers of Intel Company has been returned to the distributor because of poor quality of screen performance when it is running. Suppose that

If the envelope is fed improperly into the machine, the contents of the envelope may not be removed or may be damaged. In this case, the machine is said to have “failed.”

(a) If the machine has a probability of failure of 0.01, what is the probability of more than 1 failure occurring in a batch of 20 envelopes?

(b) If the probability of failure of the machine is 0.01 and a batch of 500 envelopes is to be opened, what is the probability that more than 8 failures will occur?

Question 16:

The exponential distribution is frequently applied to the waiting times between successes in a Poisson process. If the number of calls received per hour by a telephone answering service is a Poisson random variable with parameter λ = 6, we know that the time, in hours, between successive calls has an exponential distribution with parameter β =1/6. What is the probability of waiting more than 15 minutes between any two successive calls?

Question 17:

The lifetime, in weeks, of a certain type of transistor is known to follow a gamma distribution with mean 10 weeks and standard deviation √50

(b) What is the probability that response time exceeds 10 seconds?

Question 19:

The number of automobiles that arrive at a certain intersection per minute has a Poisson distribution with a mean of 5. Interest centers around the time that elapses before 10 automobiles appear at the intersection.

(a) What is the probability that more than 10 automobiles appear at the intersection during any given minute of time?

(b) What is the probability that more than 2 minutes elapse before 10 cars arrive?

(c) What is the probability that more than 1 minute elapses between arrivals?

(d) What is the mean number of minutes that elapse between arrivals?

Name: ________________________ Std ID: ________________________ Sec: ____________

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Question 20:

In a biomedical research study, it was determined that the survival time, in weeks, of an animal subjected to a certain exposure of gamma radiation has a gamma distribution with α = 5 and β = 10.

(a) What is the mean survival time of a randomly selected animal of the type used in the experiment?

(b) What is the standard deviation of survival time?

(c) What is the probability that an animal survives more than 30