Final test XSTK - Lý thuyết xác suất và thống kê FTU

FINAL TEST Question 1: A box contains 10 balls: 4 red and 6 blue. A second box contains 16 red balls and an unknown number of blue balls. The probability that both balls are the same color is 0.44. Find the number of blue balls in the second box. Question 2: The number of pages printed before replacing the cartridge in a laser printer is normally distributed with a mean of 113000 pages and a standard deviation of 600 pages. A new cartridge has just been installed. a. What is the probability that the printer produces more than 12000 pages before this cartridge must be replaced b. What is the probability that the printer produces fewer than 10000 pages Question 3: In a survey conducted to determine, among other things,the cost of vacations, 164 individuals were randomly sampled.Each person was asked to compute the cost of her or his most recent vacation. The average cost of the survey is $200. Assuming that the standard deviation is $400. Estimate with 95%confidence the average cost of all vacations. Question 4: The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers, she guesses that the standard deviation is 6 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds? Assume that the confidence level is 90% Question 5: A random sample of 10 young adult men(20-30 years old)was sampled.Each person was asked how many minutes of sports he watched on television daily.The responses are listed here: 50,65,58,55,52,63,59,57,74,65. It is known that σ = 9.Test to determine at the 5% significance level whether there is enough statistical evidence to infer that the mean amount of television watched daily by all young adult men is greater than 50 minutes.