The resting heart rate for an adult horse should average about μ = 43 beats per minute. Let x be a random variable that represents the resting heart rate for an adult horse. Assume that x has a distribution that is approximately normal, with standard deviation σ = 10.5.
(a) What is the probability that the heart rate is less than 25 beats per minute? (Round your answer to four decimal places.)
(b) What is the probability that the heart rate is greater than 60 beats per minute? (Round your answer to four decimal places.)
(c) What is the probability that the heart rate is between 25 and 60 beats per minute? (Round your answer to four decimal places.)
(d) A horse whose resting heart rate is in the upper 12% of the probability distribution of heart rates may have a secondary infection or illness that needs to be treated. What is the heart rate corresponding to the upper 12% cutoff point of the probability distribution? (Round your answer to the nearest whole number.)

(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?