Suppose a certain medical treatment is effective in 80% of the cases treated. Let Y denote the number of patients for which the treatment is effective in a random sample of 100 patients, Bin(n, p) with n = 100 and p = 0.8. Find an approximate probability that so that Y~ 75
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- What is the probability that the part lasts less than 1 hour?A lot of 75 washers contains 6 defectives whose variability in thickness is unacceptably large. A sample of 10 washers is selected at random without replacement a. Find the probability that at least one unacceptable washer is in the sample b. Calculate the mean of (x) c. Calculate the standard deviation of (x)According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 48 minutes and a standard deviation of 5.8 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient and let X be the average time between taking a pain reliever and getting relief for a random sample of size 43. 1. Describe the probability distribution of X and state its parameters u and o: X- Select an answer and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 53 minutes. (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem Select an answer to describe the probability distribution of X and state its parameters uz and oy: (Round the answers to 1 decimal place) X - Select an answer v (µx ,ox = and find the probability that the average time between taking a pain reliever and getting…
- the environmental protection agency (EPA) limits the amount of vinyl chloride in the plant air emission to no more than 10 parts per millions. suppose a mean emission of vinyl chloride for a partiular plant is 4 parts per million. assume the number of parts per million of vinyl chloride in air sample x follows a Poisson probability distribution what is the standard deviation of the plant is it likely that a sample of air from the plant would yield a value of x that would exceed the EPA limit? explain. note that P(x <=9)= 0.991868Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?8% of all cars fail the emissions inspection, find the probability that in a sample of 85 cars, 11 will fail. Use the Poisson approximation to Find the mean number λ of cars that fail the emissions inspection in a sample of 85 cars.
- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by 29 lb.(a) If 1 woman is randomly selected, find the probabity that her weight is between 113 lb and 172 lb(b) If 3 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lb(c) If 73 women are randomly selected, find the probability that they have a mean weight between 113 lb and 172 lbThe taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 2.8 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. USE SALT (a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) 0.5432 (b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
- Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal, For the population of healthy female adults, suppose the mean of the x distribution is about 4.64, Suppose that a female patient has taken six laboratory blod tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 () Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) C) Do the given data indicate that the pooulation mean RBC count for this patient is lower than 4.647 Use a- 0.05. (a) What is the level of significance? State the nul and alternate hypotheses. O Hn: 4- 4.64; H: 4.64 O Ho: H> 4.64; H:u- 4.64 O Hn: H- 4.64; H: H 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal,…Let Y1....,Yn be a random sample from a normal distribution with mean 30 and standard deviation 3. What is the probability the largest observation is greater than 30?
