If X is normally distributed with mean of 100 and standard deviation of 10. What is the P(70
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Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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- Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P( – b < Z < b) = 0.7062, find b. Round your answer to 2 decimals. b =Show Consider the following hypothetical situation. Grade data indicat4es that on the average 27% of the students in senior engineering classes have received A grades. From past data we have measured a standard deviation of 15%. We would like to model the proportion X of A grades with a beta distribution. a. Please also provide the values of theparameters. b. Use the distribution in (a) to find the probability that more than 32% of the students had an A.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(−0.9<z<b) = 0.5607, find b.
- The length of time, X hours that a phone will work before it needs charging is normally distributed with amean of 120 hours and a standard deviation of 20 hours. Find the value of d such that P XS2. Assume that x₁,...,10 € R satisfy ₁₁ = 3 and ΣΩ1x? standard deviation of ₁,... , X10? i=1 i=1 (This question appeared as is in May 2018 exam) = 10. What is the sampleUse the formula to find the standard error of the distribution of differences in sample means, I1 – X2. Samples of size 110 from Population 1 with mean 82 and standard deviation 14 and samples of size 80 from Population 2 with mean 76 and standard deviation 17 Round your answer for the standard error to two decimal places. standard error = iAssume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(-b<z<b)=0.9716, find b.If X is normally distributed with mean of 60 and standard deviation of 5. What is the P(55Assume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the following: a. P(Z < 13) b. P(Z > 9) c. P(6 < X < 14)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. Let Z represent the reading of this thermometer at freezing. What reading separates the highest 46.73% from the rest? That is, if P(z > c) = 0.4673, find c. c = °CA B. The mean blood cholesterol level for all men aged 20 to 34 years is p = 188 mg/dl with a standard devlation of a = 41 mg/dl. We suspect that the mean for cross-country runners is lower. A random sample of 20 cross-country runners yielded a mean level of 172 mg/di. SHOW YOUR FORMULAS AND ALL WORK ON THIS PAGE What is the standard deviation of the mean length X? Standard Deviation 41.0000Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(−b<z<b)=0.945, find b.b=Recommended 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