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Please samplers the following four questions 1. Consider the standard normal distribution with mean ,u = 0 and standard deviation 0 = 1. (a) What is the probability that an outcome 2 is greater than 2.30? (b) What is the probability that z is loss than 1.45? (c) What is the probability that z is between - l .60 and 3.10? {d} What value of z cuts off the upper 15% of the distribution? (e) What value of 2 marks off the lower 20% of the distribution? A hospital administrator has been asked by her supervisor to assess whether waiting time in the emergency room (ER) has changed from last year, when average wait time was 127 minutes. The administrator collects a simple random sample of 64 patients and records the time between when they checked in at the ER until they were rst seen by a doctor; the average wait time is 13'}' minutes, with standard deviation 39 minutes. (:1) Compute and interpret a 95% condence interval for mean ER wait time at the hospital. Based on the interval, is mean ER wait time signicantly different from 127 minutes at then = 0.05 level? (b) Would the conclusion in part a) change if the signicance level were changed to a = 0.01? (c) Suppose that upon seeing the results from part a), the supervisor criticizes the hospital administrator on the basis that ER wait times have increased greatly from last year and the administrator must be at fault. Present a brief argument in favor of the administrator; besure to fully explain your reasoning. The World Health Organization denes osteoporosis in young adults as a measured bone mineral density 2.5 or more standard deviations below the mean for young adults. Assume that bone mineral density follows a normal distribution in young adults. What percentage of young adults suffer from osteoporosis according to this criterion? The 2010 General Social Survey asked the question: \"For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% condence interval of 3.40 to 4.24 days in 2010. (a) Interpret this interval in context of the data. (b) What does \"95% condent" mean? Explain in the context of the application