Suppose that 10% of the engines manufactured on a certain assembly lineare defective. If engines are randomly selected one at a time and tested,

(a) (4 points) Calculate the probability that two good engines will be testedbefore a defective engine is found.

(b) (4 points) Calculate the probability that at least three good engineswill be tested before a defective engine is found.

(c) (2 points) Calculate the expected value of the number of good enginestested before a defective engine is found.

1.Suppose small aircraft arrive at a certain airport at a rate of 8 per hour. What is the probability that at least 13 small aircrafts arrive during a given hour?

2.A particular telephone number is used to receive both voice calls and fax messages. Suppose that 30% of the incoming calls involve fax messages. Consider a sample of 20 incoming calls, what is the probability that at most 6 of the calls involve a fax message.

A production company are going to run the entire factory from a controll-room. In the control-room there is several controllboards that in the initial period sets of false alarms. In average it sets of two false alarms per hour. The number of false alarms are poisson distributed.

a) What is the probability that there is excactly ten false alarms during a 8 hour workday?

b) What is the probability that it goes more than one hour before the next false alarm?

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is six. Find the probability that​ (a) exactly five typographical errors are found on a​ page, (b) at most five typographical errors are found on a​ page, and​ (c) more than five typographical errors are found on a page.

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is six. Find the probability that​ (a) exactly five typographical errors are found on a​ page, (b) at most five typographical errors are found on a​ page, and​ (c) more than five typographical errors are found on a page.

Around 16% of all ABC college students are declared econ majors. a sample of 75 students is taken.

(1) What is the distribution of the proportion of econ majors in your sample? (sampling distribution)

(2) What is the exact distribution of the number of econ majors in your sample?

(3) What’s the probability that more than a quarter of the students you sample are majoring in econ

(4) What’s the probability that less than 10% of the sample will be econ majors?

5.26 A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Consider a sample in which 300 people are randomly selected who have fractured or dislocated a bone. a. What is the probability that exactly five of them did not see a doctor? b. What is the probability that fewer than four of them did not see a doctor? c. What is the expected number of people who would not see a doctor?

1) Assume that for a recent 41-year period there were 5469 earthquakes which were considered as “strong” earthquakes. Using a Poisson distribution, find the probability that in a given year, there are exactly 150 earthquakes that are considered “strong”.

2) Assume that the mean number of aircraft accidents in the United States is 8.5 per month and that a Poisson distribution applies. Find P(5), the probability of having 5 accidents in a month. Is it unlikely to have a month with 5 accidents?

Example: 9) An article states that false-positives in polygraph tests (tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about 20% of the time. Suppose that such a test is given to 10 trustworthy individuals. (Round all answers to four decimal places.)

a) What is the probability that all 10 pass?

b) What is the probability that more than 2 fail, even though all are trustworthy?

Example: 9) Suppose that 40% of the students who drive to campus at your university carry jumper cables. Consider the random variable x = number of students who must be stopped before finding a student with jumper cables This is a geometric random variable with p = . Thus the probability distribution of x is p(x) = ( )^x−1 ( ) ^x = 1, 2, 3, . . . Using the above probability distribution find the following probabilities:

a) p(1) =

b) p(2) =

c) P(x ≤ 4) =

c) The article indicated that 500 FBI agents were required to take a polygraph test.

Consider the random variable x = number of the 500 tested who fail.

If all 500 agents tested are trustworthy, what are the mean and standard deviation of x?