A box contains 13 defective and 7 non-defective bulbs, find the probability mass function (pmf) of random variable X which represents the number of non-defective bulbs out of 5 non-defective bulbs drawn randomly.
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- In the manufacture of stainless-steel pipes, a particular production process is (b) known to yield 3 pipes with crack walls in every batch of 100 stainless-steel pipes produced. From production of 100 pipes produces, 40 samples are selected for destructive testing. Find the probability that 2 sample contains crack walls.The main exit gate has an outflow rate of 20 cars per minute which can be modeled as a Poisson Random Process. Suppose the south gate is also opened and given that cars choose it 34% of the time. What will be the new average time it takes for a car to exit the main gate? (Use 3 sf, in seconds)There are 3 blue and 2 red balls in a bag. The y random variable is the number of blue balls drawn from the bag and is the hypergeometric variable. Two balls are drawn at random. a)Calculate the variance and mean for the y variable. b)Calculate the probability that both selected balls will come blue.
- A box contains of 8 GOOD light bulbs and 2 burned out bulbs, 4 bulbs are selected randomly to put into a new lamp, compute the probability of having all 4 Good bulbs.Insulin pens used to administer a patient's insulin at hospitals have a malfunction rate of 9%. This meant that out of a box of 200 pens, 18 are defective in some way and must be discarded. a) Find the probability of randomly selecting 3 defective insulin pens in a row from a brand-new box of 200 pens if a defective pen is immediately discarded. b) Find the probability of randomly selecting 3 effective insulin pens in a row from a brand-new box of 200 pens, if an effective pen is immediately used and discarded.A railway train is fitted with three engine units that can be assumed to exhibit a constant hazard rate with a mean life of 200h. In a 15 hour working day, calculate the probability of a train having: (i) No failed engine units (ii) Not more than one failed unit.
- The spinner is spun one time. Find the probabilities. P(A) = P(C) = %3D A A E P(BUC)= P(B©) = Sample Space: P(B U A)= P(B U A)C = %3D P(D^)= P(AN C)= Page B.a manufactoring company produces 10,000 platics cups per day. This company supplies cups to a supermakret which sells them in packs of 10 per pack. Ig less than two of a ranfdomlu slected pack (of 10 cups) from the order are defective, the supermarket accepts the whole order. The proportion of defective cups produced by the manufactoring company is 10%. Let X be the random variable representing the number of defective cups in a pack. i) identify the type of distribution being described in this question and write down the value of its parameters. ii) what is the probability that the order will be accepted? iii) What is the probability that a randomly selected pack (of 10 cups) has more than two defective cups?Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 38 passengers, and a flight has fuel and baggage that allows for a total passenger 6,270 Ib load of 6,270 Ib. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than = 165 Ib. What is the probability that the aircraft is 38 overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 180.6 lb and a standard deviation of 36. The probability is approximately (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? O A. No. Because the probability is high, the aircraft is safe to fly with its current load. O B. Yes. Because the probability is high, the pilot should take action by somehow reducing…
- An item produced by a company is susceptible to two types of defects namely, A and B. The probability that anitem has defect A is 0.167. The probability that it has defectB is 0.125. Calculate the probability that the item has(i) Both A and B defects(ii) Only defect A(iii) Only defect B(iv) One defect only(v) At least one defectWhen several women are not hired at the Telektronics Company, they do some research and find that among the many people who applied, 30% were women. However, the 20 people who were hired consist of only 3 women and 17 men. Find the probability of randomly selecting 20 people from a large pool of applicants (30% of whom are women) and getting 3 or fewer women. Based on the result, does it appear that the company is discriminating based on gender?In analyzing hits by certain bombs in a war, an area was partitioned into 575 regions, each with an area of 0.15 km2. A total of 505 bombs hit the combined area of 575 regions. Assume that we want to find the probability that a randomly selected region had exactly three hits. In applying the µ^ • e Poisson probability distribution formula, P(x) = identify the values of u, x, and e. Also, briefly describe what each of those symbols х! represents. Identify the values of u, x, and e. X= and e = (Type integers or decimals rounded to five decimal places as needed.) Briefly describe what the symbol u represents. Choose the correct answer below. A. The symbol p represents a static value. B. The symbol u is a variable that represents the number of occurrences of the event in an interval. C. The symbol u is a variable that represents the mean number of occurrences of the event in the intervals. D. The symbol u is a variable that represents the area of each region. E. The symbol u is a variable…
