Densities of Metal, a world-famous rock band, put on a show at an arena in Rome last night. The rectangular floor of the arena had an area of 48,000 \text{ m}^248,000 m 2 48, comma, 000, start text, space, m, end text, squared and was packed shoulder to shoulder with fans. The band wants to know how many people were at last night's show. They estimate that, on average, each person takes up a circular space with a diameter of 0.8 \text{ m}0.8 m0, point, 8, start text, space, m, end text. Since the floor was packed, they assume these circular spaces were tightly packed together in rows and columns. Estimate how many people were at Densities of Metal's rock show based on their assumptions.

(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?