The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 10 min and standard deviation 2 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Hint: you can assume that the results of the two days are independent)
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- 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?Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 2 customers in the first line and n₂ = 13 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.1 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P =
- A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 35.2 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 35.2 weeks and that the population standard deviation is 5.6 weeks. Suppose you would like to select a random sample of 29 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.1 and 33.8. P(33.1 < X < 33.8) = 0.0475 29 is Find the probability that a sample of size n randomly selected with a mean between 33.1 and 33.8. Р(3.1 < М < 33.8) - Enter your answers as numbers accurate to 4 decimal places.Suppose the heights of 18 year old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches. What is the probability that an 18 year old man selected at random is between 70 and 72 inches tall? if random sample of twenty-nine 18 year old men is selected, what is the probability that the mean height x is between 70 and 72 inches? compare your answers to parts a and b. Is the probability in part b much higher? WhyThe length of the long-distance calls made by the employees of a certain company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.5 minutes. Find the probability that a call will last between 5 and 10 minutes. A. .3897 B. .1788. C. .6290. D. .6308
- A production line in a factory, assembles laptops. A random sample of assembly time of 36 laptops has been drawn from this factory. Suppose, the population distribution has a mean assembly time of 25 minutes and standard deviation 6 minutes. What is the probability that a sample mean is 26 minutes? Select one: a. 0.0 b. =P(Z>1) c. =P(Z=0) d. =P(Z<1) e. None of the othersSolon commutes daily from his home to school. On the average, the trip takes 84 minutes, with a standard deviation of 12 minutes. Assume that the travel time is normally distributed. He leaves his house at 7:45 am.If his next class has a quiz from 9:00 am to 9:10 am, what is the probability that he will only arrive in class at some point during the quiz?How long will his travel time be in the longest 5% of trips?Suppose that he has meetings at 9:15 am for the next four days. Find the probability that he will be late in at least two of these meetings.Suppose the time it takes for guests to wait for an elevator at the lobby of a certain office building has a uniform distribution between 0 and 4 minutes. What is the probability that, the next time you need to take this elevator, you'll have to wait at most 1.6 minutes? (Your answer should be a decimal. Round to 4 decimal places if necessary.)
- r a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 510 and a standard deviation of 170 . The grading process of this year's exam has just begun. The average score of the 40 exams graded so far is 526 . What is the probability that a sample of 40 exams will have a mean score of 526 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.In a population of statistics students it was found that the mean score on the final is 150 with a standard deviation of 20 points. Ifa student is chosen at random, what is the probability that their grade will be less than 115? O 03867 O 0.3707 O 0.9599 O 0.5987 O 0.0401A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 35.2 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 35.2 weeks and that the population standard deviation is 5.6 weeks. Suppose you would like to select a random sample of 29 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 33.1 and 33.8. Р(3.1