If a binomial distribution applies with a sample size of n = 20, find the probability of at least 7 successes if the probability of a success is 0.25. 0.2142 0.1814 0.3123 0.2333
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- The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529. State the null and alternative hypotheses for the above scenario.An operational risk analyst is using the POT methodology to estimate VaR. Parameters are provided in the following tables: Loss threshold (%) μ. = 2 Number of observations N = 1000 Observations in excess of the threshold n = 9 Scale parameter β = 0.85 Shape parameter (tail index) = 0.3 - Calculate VaR at the 99% confidence level.The matrix of transition probabilities below deals with brand loyalty to CoronaBits and CovidBits junk food. Current Next Purchase Purchase CoronaBits CovidBits CoronaBits .75 25 CovidBits 20 .80 What are the steady state probabilities? O [3/4 1/4] O [ 2/3 1/3] O [4/9 5/9] O [1/2 1/2]
- Samples of size 20 are drawn from lots of 100 items, and the lots are rejected if thenumber of defectives in the sample exceeds 2. If the true proportion of defectives inthe lot is 5 percent, determine the probability that a lot is accepted usingc. The Poisson approximation to the binomialBig Turkey Burger Farms (BTBF) produces a large turkey burger that is world famous. This burger is known not only for its quality, but also its size and consistency. BTBF produces a turkey burger that on average is 12 ounces (with a standard deviation of 0.10 ounces). Currently, BTBF has been approached by two major restaurant chains: Monarch Burgers and Audrey's. a. Monarch wants a turkey burger that is between 11.77 and 12.23 ounces. i. For this customer, calculate the Cp. ii. Calculate the Cpk value. iii. How well would BTBF's products meet the demands of Monarch Burgers? b. Audrey's, in contrast, wants a turkey burger that is 11.95 ounces on average with a tolerance of ± 0.30 ounces. i. For this customer, calculate the Cp. ii. Calculate the Cpk value. iii. How well would BTBF's products meet the demands of Audrey's?A toy manufacturer wants to see how long, on average, a new toy captures children's attention. He tests 17 children selected at random and finds that their mean attention span is 27 minutes with a standard deviation of 5 minutes. If we assume that attention spans are normally distributed, find a 90% confidence interval for the mean attention span of children playing with this new toy. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.) Lower limit: Upper limit:
- Balance the equation. Fill in the blank. If a coefficient is 1, write a 1 (i.e. do not leave it blank). Al2O3 + Al + Fe Fe3O4 =Based on a random sample of size 75, you observe a sample mean of 85.63 and a sample standard deviation of 19.71. Which of the following are the endpoints of a 90% confidence interval for the population mean? (Because of potential roundoff, choose the closest.) a. 82.69 to 88.57 b. 81.84 to 89.42 c. 79.61 to 91.65 d. 81.10 to 90.16Consider the MA(1) series X, = W, + 0.5W-1, where W, ~ WN (0,1). Please use the Innovation Algorithm to give the one-step-ahead prediction X = P,X for n = 1,2,3, and 4. Is 0, closer to 0.5 for n=4? n+1