Suppose that the survey is distributed to 135 individuals and an estimated 40% of the population supports the change. Lastly, calculate the probability that 45 of the 135 respondents support the rezoning. Express your answer with four decimal places, and don't forget about the Continuity Correction Factor!
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- A multiple-choice examination consists of 100 questions, each having possible choices a,b,c, and d. Approximate the probability that a student will get fewer than 28 answers correct if he randomly guesses at each answer. (Note that, if he randomly guesses at each answer, then the probability that he gets any one answer correct is 0.25. ) Use the normal approximation to the binomial with a correction for continuity. Round answer to at least 3 decimal places. Do not round any intermediate steps.A geneticist, in assessing data that fell into two phenotypicclasses, observed values of 250:150. He decided to perform chisquare analysis using two different null hypotheses: (a) the datafit a 3:1 ratio; and (b) the data fit a 1:1 ratio. Calculate the x2values for each hypothesis. What can you conclude about eachhypothesis?A random sample is selected from a normal population with a mean u = 30 and standard deviation sima = 8 . After a treatment is administered to the individuals in the sample, the sample mean is found to be M =33. a) if the sample consist of n=16 scores is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with alpha spaceequals space 0.05. b) if a sample consists of n= 64 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed with alpha space equals space 0.05. c) comparing your answers for parts a and b explain how the size of the sample influences the outcome of the hypothesis test?
- Suppose the distribution of some random variable X is modeled as Negative binomial with parameters, p and r, where p is the probability of success and r is the total number of success over the trials. Find the method of moment (MM) estimators for (p,r), in closed algebraic form expressions based on a random sample of size n, X1, X2,...,Xn.in agenetic experiment on peas one sample of offspring contained 366 green peas and 428 yellow peas based on those results estimate the probality of getting an offspring pea that os green is the result reasnably close to the value of 3/4 that was expectedIf it can be assumed that the binomial parameter θassumes a value close to zero, upper confidence limits ofthe form θ < C are often useful. For a random sample ofsize n, the one-sided intervalθ <12nχ2α,2(x+1) has a confidence level closely approximating (1 − α) 100%. Use this formula to find a 99% upper confi-dence limit for the proportion of defectives produced by a process if a sample of 200 units contains threedefectives.
- A company manufactures bulbs. The probability of getting a defective bulb is 0.055. A sample of 100 bulbs were selected. Use Poisson approximation to binomial distribution to find the probability of finding at most 3 non-defective bulbs.A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failedbeams are randomly selected and the type of failure is determined for each one. Let X= the number of beams among the three selected that failed by shear. List eachoutcome in the sample space along with the associated value of XA manufacturing process produces semiconductor chips with a known failure rate of 7.5%. If a random sample of 265 chips is selected, approximate the probability that more than 16 will be defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.
- # TODO 2: Use the Matplotlib plt.hist() method to display area values. All we have to do is supply area_values to the plt.hist() method, and it will compute the bins for us. # TODO 2 plt.show() Expected Output:A manufacturing process produces semiconductor chips with a known failure rate of 7.6% . If a random sample of 240 chips is selected, approximate the probability that at least 18 will be defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.Suppose that a new treatment is successful in curing a common ailment 73% of the time. If the treatment is tried on a random sample of 100 patients, approximate the probability that more than 70 will be cured. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)