Shelia’s doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level is above 136 milligrams per deciliter (mg/dl) one hour after ingesting a sugary drink. Shelia’s measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 125 mg/dl and σ = 11 mg/dl. a)What are the mean and standard deviation of the distribution of sample proportion if measurements are made instead on 40 separate days? b)If measurements are made on 40 separate days and the mean result is compared with the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes? c)Let’s consider what could happen if we took 40 separate measurements from Shelia. What is the blood glucose level L such that the probability is only 0.15 that the average of 40 measurements is larger than L?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Shelia’s doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if her glucose level is above 136 milligrams per deciliter (mg/dl) one hour after ingesting a sugary drink. Shelia’s measured glucose level one hour after the sugary drink varies according to the
a)What are the
b)If measurements are made on 40 separate days and the mean result is compared with the criterion 140 mg/dl, what is the
c)Let’s consider what could happen if we took 40 separate measurements from Shelia. What is the blood glucose level L such that the probability is only 0.15 that the average of 40 measurements is larger than L?
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