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- A single dice has 6 sides with each side marked 1,2,3,4,5,6. if the dice is rolled 12 times, what is the probability that it will land on either 2 or 4 a total of 5 times? also determine the mean and standard deviation for this distributionWhat is the probability that total waiting time is at most 4 min? What is the probability that total waiting time is between 4 and 8 min? What is the probability that total waiting time is either less than 3 min or more than 9 min?5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate A = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. a) What is the probability that the spider catches 6 insects in two days?
- a. Enumerate 5 properties of the normal curve (in any order). b. Enumerate 5 Other Discrete Probability DistributionsIn a factory, in a batch of 100 products, there are on average 3 of defected ones. Please calculate the following using the indicated distributions: Probability of having at least 1 defected products in 900 products. a- Solve using Binomial distribution b- Solve using Poisson distributionPlease show work... and round probabilities to FOUR DECIMALS The following table summarizes results from 985 pedestrian deaths that were caused by accidents. Pedestrian Pedestrian was NOT Intoxicated intoxicated Driver was intoxicated 59 79 Driver was NOT 266 581 intoxicated If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. If two DIFFERENT pedestrian deaths are randomly selected, find the probability that they both involve intoxicated pedestrians. If we randomly select a pedestrian death, what is the probability that the pedestrian was intoxicated, given that the driver was intoxicated? If we randomly select a pedestrian death, what is the probability that the driver was intoxicated?
- Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone. What probability distribution describes this situation and what are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day? Compute to the nearest whole number.The service stations along a highway are located according to a Poisson distribution in space, with an average of 1 service station in 15 miles. There is a probability of 0.3 that a service station would have no gasoline available. What is the probability that there is at most one service stations in the next 45 miles? Please round your result to two decimal places.There are two car battery producers, such as A and B. The mean lifetimes of batteries are 1424 and 1624days from the producers of A and B, respectively. The standard deviations of the batteries from both manufacturers are 200 and 100 days for A and B, respectively. Random samples of 120 batteries from each company are selected for the test.a) Please find the probability for the Brand A batteries that the average lifetime is at most 960 days.b) Find the probability for the Brand A batteries that the average lifetime is 150 days more than the batteries from Brand B.
- 8. Final: For recent period of 100 years, there were 530 Atlantic hurricanes. Assume the Poisson distribution is a suitable model, find the probability that less than 3 hurricanes in a randomly selected year. O a. .1901 O b. None of the above O C. .2075 O d. .3701 O e..1016 日 田In a factory, in a batch of 100 products, there are on average 3 of defected ones. Please calculate the following using the indicated distributions: Probability of having at least 1 defected products in 800 products. a- Solve using Binomial distribution b- Solve using Poisson distribution5. Suppose that the number of insects caught in a spider's web in one day follows a Poisson distribution with rate = 2.6. For the questions that follow, make sure to define a random variable, state its distribution (including parameters), and translate the question into a probability statement. %3D wg probal b What is the probability that the spider catches at least one insect in 12 hours? PUS 18)
