One of the machines is causing quality problems as 5% of the engine parts produced on this machine have been found to be defective. Find the probability of finding 0, 1, 2, 3, and 4 defective parts in a sample of 50 parts (assuming a binomial distribution).
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- Suppose the scores, x, on a college entrance examination are normally distributed with a mean of 1000 and a standard deviation of 100. If you pick 4 test scores at random, what is the probability that at least one of the test score is more than 960?Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information?Suppose the scores, X, on a college entrance examination are normally distributed with a mean of 1000 and a standard deviation of 100. If you pick 4 test scores at random, what is the probability that at least one of the test score is more than 950?
- If Y is a random variable from an exponential distribution with a mean of 5; what is the probability that Y is more than 7?Suppose you did an experiment with 3 groups and 16 subjects per group. The sample variances in the three groups were 14, 16, and 18. Using Tukey's test to compare the means, what would be the two-tailed probability for a comparison of the first mean (14) with the last mean (18)?A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 550 and 60, respectively. 30 applications for this year's program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year's applicants is the same as that of 5 years ago, find the probability of erroneously concluding that there is not enough evidence to supports the claim when, in fact, the true mean GMAT score is 590. Assume a is 0.02. P(Type II Error) =
- You have a uniform distribution whose lowest value is 7 and whose highest value is 15. Find the probability that a randomly selected number from this distribution will be between 9.3 and 10.6.About 70% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 67%? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to The probability that the sample proportion surviving for at least 3 years will be less than 67% isMr. Siozios finds that the empirical probability of a student failing statistics is 30%. There are 10 students. Find the probability that at most three students fail statistics.
- Each trial in a binomial experiment has a 25% probability of success.if the normal distribution is to be used to calculate a probability for thisbinomial experiment, then number of trials must be at least(7) If the probability of a student graduating is 0.95, find the probability that more than 472 students students graduating among 500 students. (8) If the probability of a student receiving financial aid is 0.72, find the mean and variance of the number of students receiving financial aid among 40000 students. (9) There are 300 questions on a multiple choice exam. For each question there are 5 choices to choose from, and there is only one correct choice for each question. Find the mean (expected value) and variance for the number of questions you answer correctly by making random guess.You are playing Super Mario Bros together with 2 of your friends. You got to level 4, where you encounter your nemesis Bowser. Bowser is very strong, and he is defeated only 41% of the times. Each of you will play level 4 one time. Suppose that, after your friends are gone, you decide to play level 4 until you beat Bowser. Let Y be the number of times you play level What is the distribution of Y? What is the probability that you play less than 3 times? What is the expected number of times that you play? - for this answer I got 2.439 because I did E(y)=1/p = 1/0.41 = 2.439