1. You toss a coin 8 times. Call heads success. If the coin is fair, the probability of success P is 0.5. What is the probability of getting exactly 5 heads out of 8 tosses? Less than 40 heads out of 100 tosses? At least 12 heads in 20 tosses? Use the Minitab functions to represent all forms of binomial distributions.
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- Study the binomial distribution table. Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let's look for that symmetry. Consider the section of the table for which n = 5. Look at the numbers in the columns headed by p = 0.30 and p = 0.70. Do you detect any similarities? Consider the following probabilities for a binomial experiment with five trials. (c). For what value of r is P(r successes) the same using p = 0.70? r = ? (d) What column is symmetrical with the one headed by p = 0.20? Choose one of the statements:A. the column headed by p = 0.85 B. the column headed by p = 0.70 C. the column headed by p = 0.50 D. the column headed by p = 0.40 E. the column headed by p = 0.80Metalworks manufactures metal sheets via its factory that operates 5x a week. During quality control phase, on average, there is 1 hairline crack in every 10 square feet of metal produced. What is the probability that three or more cracks will appear in a 5x8 foot metal panel?a. describe random variable Xb. what distribution does X follow? explainc. What is the probability that three or more flaws will appear in a 5x8 foot metal panel?62% of adults in a population have an HDTV in their home. You randomly select 45 adults and ask them if they have an HDTV in their home. What is the probability that at most 20 of them respond yes? Use binomial distribution and normal distribution approximation. Compare your results.
- Female dart cat make 2.3 calls/min at night. Calls occur randomly and are independent of one another. For any given dart cat you encounter at night, what is the probability that it will call 2 times in a one minute period? It’s the Poisson distribution equation.5 Use the Binomial Distribution to calculate the probability that Lisa was hit by 3 or fewer rotten eggs from Liana.Use the scenario below to determine the correct values of n, p, q and x of the binomial distribution. Suppose that in a certain video game there is a 5.1% item drop rate of wild meat after defeating a Beast Master. Assume 14 Beast Masters are defeated. What is the probability that 5 wild meats will drop? n = p = q = X =
- In the winter, guests who visit Yosemite National Park like to stay at an overnight lodge in the park 71 % of the time. Find the probability that among 11 guests surveyed exactly 3 guests like to stay at an overnight lodge in the park. P(x = 3) =After careful research you observe that the number of hackers active on each day is a random variable Bin(3,0.5) distribution. If no hackers are active, the probability of the website failure is 0.15; If one hacker is active the probability of the website failure is 0.3; if two or more hackers are active the probability of the website failure is 0.5. You conclude that the total probability of website failure on a given day is two decimal place). Assuming there is a failure, the probability no hackers are active is (to (to two decimal places).Determine whether the random variable X has a binomial distribution. If it does, state the number of trials n. If it does not, explain why not. Twenty students are randomly chosen from a math class of 70 students. Let X be the total number of student absences.
- A bag contains 10 cards, of which 2 are marked two, 1 is marked three, 4 are marked four and 3 are marked five. Construct a probability distribution table, showing X, the number on the card. The tables has been constructed. It is attached. Can you help with part ii. Use your table to find the variance of this probability distribution. ?32% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Complete parts (a) (a) Construct a binomial distribution using n=6 and p=0.32. x P(x) 0 1 2 3 4 5 6 (Round to the nearest thousandth as needed.)