The moment generating function of the negative binomial distribution is given by pe' m, ()=1-ge 1- qe' Derive the mean of the distribution using the mgf.
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- For each letter, represent in a normal curve.Find the following probabilities. It may help to sketch the pdf for Standard Normal Distribution and shade in the area that corresponds to the probability of interest. X ~ Norm(266, 16^2), find Pr(X < 200)If X ~B(80,0.2), use the normal distribution to approximate the binomial distribution for: (ii) P(14≤X≤18)
- assume that X is normally distributed with a mean 150 and standard deviation of 40. find the probability that (A) x is less then 145 and (B) x is grater then 170assume that X is normally distributed with a mean 180 and standard deviation of 56. find the probability that (A) x is less then 115and (B) x is grater then 154Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 265 feet and a standard deviation of 40 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 264 feet. Round to 4 decimal places.
- The average THC content of marijuana sold on the street is 10.4%. Suppose the THC content is normally distributed with a standard deviation of 1%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 10.3. c. Find the 75th percentile for this distribution. %Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than -1.171°C.P(Z < − 1.171)=Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 275 feet and a standard deviation of 35 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 265 feet. Round to 4 decimal places.
- A 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.Assume that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C. A thermometer is randomly selected and tested. Find the probability of each reading in degrees.(a) Between 0 and 1.64: (b) Between −2.89 and 0: (c) Between −1.78 and 1.03: (d) Less than −2.79: (e) Greater than 2.62:The average THC content of marijuana sold on the street is 10.9%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 10.8. c. Find the 79th percentile for this distribution. %