The risk of coronary disease for diabetes patients is related not only to the mean glucose level in the bloodstream but also to the standard deviation.
a. A diabetes patient we will call Frank posted online that his blood glucose has mean 93.1 mg/dL and standard deviation 41.5 mg/dL. Dr. Irl B. Hirsch recommends that diabetes patients regulate their glucose levels so that the Ages of Veteran Patients Undergoing standard deviation is at most 1/2 the mean. Has Frank met this recommendation?
b. Dr. Hirsch says that, ideally, the standard deviation of blood glucose levels should be at most 1/3 the mean. Has Frank met this stricter goal?
c. Frank posted that 33% of his glucose blood readings were between 79 and 121 mg/dL. What would the percentage have been if his readings were normally distributed? Recall that the mean is 93.1 mg/dL and the standard deviation is 41.5 mg/dL.
d. Glucose levels tend to be low just before meals and high just after meals. If Frank measured his blood glucose levels only just before meals and just after meals, would the data he collected be unimodal, bimodal, or multimodal? Would the data be normally distributed? Explain why that might account for the error in the result you found in part (c).