02 May Exercise 1: Entry to a certain University is determined by a national te
Exercise 1: Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 520 and a standard deviation of 80. Use R commands to answers the following questions.
(a) Tom wants to be admitted to this university and he knows that he must score better than at least 75% of the students who took the test. Tom takes the test and scores 595. Will he be admitted to this university?
(b) Alex takes the test and scores 600. What is the probability that a randomly selected person who take the test scores higher than Alex?
Exercise 2: On the average, a certain computer part lasts 7 years. The length of time the computer part lasts is exponentially distributed. Use R commands to answer the following questions.
(a) What is the probability that a computer part lasts more than 8 years??
(b) Eighty percent of computer parts last at most how long?
Exercise 3: The life time of a laser (in hours) is exponentially distributed with ? = 1/80. Two such lasers are operating independently. Use R commands to answer the following questions.
(a) Simulate 1000 numbers from exponential distribution as sample life time for each laser.(b) Estimate the probability that the sum of the two lifetimes is greater than 100 hours.(Hint: calculate the proportion of lifetime pairs in (a) satisfy sum greater than 100)
(c) Estimate the probability that the both lasers last more than 50 hours. (Hint: calculate the proportion of lifetime pairs in (a) satisfy both greater than 50)
Exercise 4: Based on weighting the most animals in the population, the American Angus Association reported that mature Angus cows had a mean weight of 1300 pounds with a standard deviation of 150 pounds. A research randomly measures 50 mature Angus cows. Use R commands to answers the following questions.
(a) Find the probability that the average weight of the 50 mature Angus cows is greater than 1320 pounds.
(b) Find the probability that the average weight of the 50 mature Angus
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