The manager at a fine arts theater has to fit 12 different performances into the upcoming season's schedule. Of all the performances, 4 are tragic play performances. If the manager randomly selects 7 shows to be performed during the first half of the season, what is the probability that exactly 2 of the chosen performances are tragic play performances?

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?

The taxi fare in gotham city is $2.40 for the first 1 2 12 mile and additional mileage charged at the rate $0.20 for each additional 0.1 mile. you plan to give the driver a $2 tip. how many miles can you ride for $10?

If the average of x,y and z is 15 what is their sum