A group of 5 men are meeting for lunch.

(a) Each of the 5 men is wearing a coat when they enter the restaurant. Upon arrival, they each give their coat to the hostess. However, the hostess forgets to take note of which coat belongs to which man so she decides to guess. If the hostess randomly passes the 5 coats back to the 5 men when they leave, what is the probability that each man gets the correct coat?

(b) Suppose now that only 2 of the 5 men is wearing a coat when they enter. Again, the hostess is forgetful and cannot remember which 2 men were wearing coats, much less which coat belongs to each of these 2 men. So, once again, she must guess. When they are ready to leave, the hostess randomly picks 2 men who she believes were wearing coats and then gives the 2 coats back to these 2 randomly picked men. What is the probability that each of the 2 coats will be returned to the correct owner? (In other words, the hostess has to first pick the correct 2 men from the group of 5 men, and then she has to give the correct coats back to each of these 2 men.)

Overproduction of uric acid in the body can be an indication of cell breakdown. this may be an advance indication of illness such as gout, leukemia, or lymphoma.† over a period of months, an adult male patient has taken nine blood tests for uric acid. the mean concentration was x = 5.35 mg/dl. the distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.87 mg/dl. (a) find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. what is the margin of error? (round your answers to two decimal places.) lower limit upper limit margin of error (b) what conditions are necessary for your calculations? (select all that apply.) σ is unknown n is large σ is known normal distribution of uric acid uniform distribution of uric acid (c) interpret your results in the context of this problem. there is not enough information to make an interpretation. the probability that this interval contains the true average uric acid level for this patient is 0.05. the probability that this interval contains the true average uric acid level for this patient is 0.95. there is a 95% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. there is a 5% chance that the confidence interval is one of the intervals containing the population average uric acid level for this patient. (d) find the sample size necessary for a 95% confidence level with maximal margin of error e = 1.10 for the mean concentration of uric acid in this patient's blood. (round your answer up to the nearest whole number.) blood tests