Let y be a random variable having a normal distribution with a mean equal to 250 and a standard deviation equal to 50. Find the following probabilities: Find k such that P(250 – k
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![Let y be a random variable having a normal distribution with a mean equal to 250 and a
standard deviation equal to 50. Find the following probabilities:
Find k such that P(250 – k<y< 250 + k = .60](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F702f32c5-3345-4dd6-bb10-5307dedbb401%2F43ea35c6-ad14-4cec-9829-a284e11ee0a7%2Fun3ihwl_processed.jpeg&w=3840&q=75)
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- Assume that we have two normal distributions both with means 0 and standard deviations σ1 and σ2. If σ1 ≥ σ2, then which of P (0 ≤ x ≤ σ1) and P (0 ≤ x ≤ σ2) is bigger? Explain your answer.Q7. A random variable X with a mean of 2.5 follows an exponential distribution. Find the following probabilities: (a) P(X > 2.5), (b) P(X xo) = 0.05.Let x be a normal random variable with its mean equal to 75 and standard deviation equal to 8. Find the following probabilities for this normal distribution. PI57Find the 95% confidence interval for the population mean if the sample is × = 70.4 and the sample size is n = 24. Assume that the population is normally distributed and the sample standard deviation is 0 = 5. Left Left: Right:X is a discrete random variable with the following PMF: P(X = -9.2) = 0.25 P(X = -2.5) = 0.25 P(X = 7.7) = 0.5 Find the standard deviation of X.Assume that the readings at freezing on a batch 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 between 0.609°C and 2.408°C. P(0.609 < Z < 2.408) =Let x be a random variable that has a normal distribution with a mean of 40 and a standard deviation of 5. After converting the following x-values to z-values, find the following probabilities: P(x < 49) P(x > 55)Let X be a normally distributed random variable with mean u = 27 and standard deviation o = 2. Calculate P(X < 21). Calculate P(25Suppose that the random variable z has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point. a) z(-0.01)b) z(-0.05)c) z(-0.10)Assume that the readings at freezing on a batch 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 between 2.857°C and 3.191°C. P(2.857 < Z < 3.191) =For a Normal Random Variable X with a mean of 80 and a Standard Deviation of 7, find P(80A random sample of size n1 =15 is selected from a normal population with a mean of 76 and standard deviation of 9. A second random sample size n2 =10 is taken from another normal population with mean 71 and a standard deviation 13. Let x barı and x bar2 be the sample means. Find: a. The probability that xbar1 – xbar2 exceeds 4.5 b. The probability that 3.5 s xbar1– xbar2 s 5.5SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman