Find the mean and the standard deviation of the normallydistributed random variable X if P(2.2≤X≤4.5)=0.35 and P(X≤2.2)=0.4.
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A: Here, µ = 207, σ = 1.5.
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A: Given, mean (µ)= 31 standard deviation (σ) = 4 sample size(n) = 34
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Q: Find the probability of z greater than 0.5 if mean is 0 and standard deviation is 1.
A: Given, Mean=0 S.D=1 P(z>0.5)=?
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- At a large manufacturing company the mean age of workers is 38 years, and the standard deviation is 6.2. Assuming the variable is normally distributed. If a random of 44 workers is selected, find the probability that the mean age of the workers in the sample is between 36 and 40 years.In a recent study, the Centers for disease Control and prevention reported that diastolic blood pressurers of adult women in the U.S. are approximately normally distributed with mean 80 and standard deviation 10.now let x be diastolic blood pressures of adult women in the U.S. find the probability that the diastolic blood pressure of a randomly chosed adult women in U.S. equals 80. a. P(X-80)= b. find the value k, so that the probability that the diastolic blood pressure of randomly chosen adult woman in the U.S. is greater than or equal to the value k. becomes 0.7777 c. find the value m, so that the probablity that the diastolic blood pressure of a randomly chosen adult woman in the U.S. is less than the value, m, becomes 0.2223A leading magazine reported at one time that the average number of weeks an individual is unemployed is 19 weeks. Assume that for the population of all unemployed individuals the length of unemployment is normally distributed where the population mean length of unemployment is 19 weeks and that the population standard deviation is 8 weeks. Suppose you would like to select a random sample of 30 unemployed individuals for a follow-up study.Find the probability that a single randomly selected value is less than 18. P(X < 18) = Find the probability that a sample of size n=30 is randomly selected with a mean less than 18. P(M < 18) = Enter your answers as numbers accurate to 4 decimal places.
- The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.39. There is 46 student in the class. Each student does his/her homework independently. What is the standard deviation of X, where X is the number of students who submit the homework on time?The probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.12. There is 35 student in the class. Each student does his/her homework independently. What is the standard deviation of X, where X is the number of students who submit the homework on time?Let x be a random variable that represents the commute time of teachers in a large rural area. If x is normally distributed with a mean of 64 minutes and a standard deviation of 12.2 minutes, find the probability that a commute time is greater than 70 minutes.
- When X is a binomial random variable, the standard deviation of the probability distribution = the square root of npq If X is a binomial random variable, where there are 196 trials, and p = 0.252 find the standard deviation.The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that X is less than 9.66 is 0.67, then what is the standard deviation of X?
- Suppose that average rainfall in your city is normally distributed, and for the past 36 months, the rainfall has been 0.5 inches per day on average with a standard deviation of 0.16. Let x be a random variable that has a normal distribution and represents the rainfall in inches per day. Using a 0.05 level of significance, you want to test the hypothesis that monthly rainfall has been 0.7 inches per day on average. What conclusion do you make from your test? Select one: a. Reject H0; the average rainfall is not 0.5 inches. b. Reject H0; the average rainfall is not 0.7 inches. c. Do not reject H0; the average rainfall is still 0.5 inches. d. Do not reject H0; the average rainfall is still 0.7 inches.The population of weights for men attending a local health club is normally distributed with a mean of 184-lbs and a standard deviation of 28-lbs. An elevator in the health club is limited to 32 occupants, but it will be overloaded if the total weight is in excess of 6240-lbs.Assume that there are 32 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?average weight = lbsWhat is the probability that one randomly selected male health club member will exceed this weight?P(one man exceeds) = (Report answer accurate to 4 decimal places.)If we assume that 32 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded?P(elevator overloaded) = (Report answer accurate to 4 decimal places.)If the evelator is full (on average) 2 times a day, how many times will the evelator be overloaded in one (non-leap) year?number of times overloaded = (Report answer rounded to the nearest…A leading magazine, (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 31 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 31 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 34 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is less than 30. P(X < 30) = Find the probability that a sample of size n = 34 is randomly selected with a mean less than 30. P(M < 30) = Enter your answers as numbers accurate to 4 decimal places. Submit Question % & 3 6 7 y 60 00 %24 4