Let
x
be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old,
x
has a distribution that is approximately normal, with mean ? = 81 and estimated standard deviation ? = 45. A test result
x
< 40="" is="" an="" indication="" of="" severe="" excess="" insulin,="" and="" medication="" is="" usually="">
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?
Hint: See Theorem 6.1.
What is the probability that x < 40?="" (round="" your="" answer="" to="" four="" decimal="">
Explain what this might imply if you were a doctor or a nurse. (Select one of the options in screenshot)
Extracted text: Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean u = 81 and estimated standard deviation o = 45. A test result x < 40="" is="" an="" indication="" of="" severe="" excess="" insulin,="" and="" medication="" is="" usually="" prescribed.="" n="" use="" salt="" (a)="" what="" is="" the="" probability="" that,="" on="" a="" single="" test,="" x="">< 40?="" (round="" your="" answer="" to="" four="" decimal="" places.)="" 0.1811="" (b)="" suppose="" a="" doctor="" uses="" the="" average="" x="" for="" two="" tests="" taken="" about="" a="" week="" apart.="" what="" can="" we="" say="" about="" the="" probability="" distribution="" of="" x?="" hint:="" see="" theorem="" 6.1.="" o="" the="" probability="" distribution="" of="" x="" is="" not="" normal.="" o="" the="" probability="" distribution="" of="" x="" is="" approximately="" normal="" with="" uz="81" and="" o,="31.82." o="" the="" probability="" distribution="" of="" x="" is="" approximately="" normal="" with="" uz="81" and="" oz="22.50." what="" is="" the="" probability="" that="" x="">< 40? (round your answer to four decimal places.) (c) repeat part (b) for n = 3 tests taken a week apart. (round your answer to four decimal places.) 0.0572 (d) repeat part (b) for n = 5 tests taken a week apart. (round your answer to four decimal places.) 0.0211 (e) compare your answers to parts (a), (b), (c), and (d). did the probabilities decrease as n increased? o yes o no explain what this might imply if you were a doctor or a nurse. o the more tests a patient completes, the weaker is the evidence for lack of insulin. o the more tests a patient completes, the stronger is the evidence for lack of insulin. o the more tests a patient completes, the stronger is the evidence for excess insulin. 40?="" (round="" your="" answer="" to="" four="" decimal="" places.)="" (c)="" repeat="" part="" (b)="" for="" n="3" tests="" taken="" a="" week="" apart.="" (round="" your="" answer="" to="" four="" decimal="" places.)="" 0.0572="" (d)="" repeat="" part="" (b)="" for="" n="5" tests="" taken="" a="" week="" apart.="" (round="" your="" answer="" to="" four="" decimal="" places.)="" 0.0211="" (e)="" compare="" your="" answers="" to="" parts="" (a),="" (b),="" (c),="" and="" (d).="" did="" the="" probabilities="" decrease="" as="" n="" increased?="" o="" yes="" o="" no="" explain="" what="" this="" might="" imply="" if="" you="" were="" a="" doctor="" or="" a="" nurse.="" o="" the="" more="" tests="" a="" patient="" completes,="" the="" weaker="" is="" the="" evidence="" for="" lack="" of="" insulin.="" o="" the="" more="" tests="" a="" patient="" completes,="" the="" stronger="" is="" the="" evidence="" for="" lack="" of="" insulin.="" o="" the="" more="" tests="" a="" patient="" completes,="" the="" stronger="" is="" the="" evidence="" for="" excess="">