A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=147 mg/dl and σ=8 mg/dl, Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:Once? n=#+2 times, where # is the last digit of your student ID?n=#+4 times, where # is the last digit of your student ID?Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

Given Information: A person is classified having gestational diabetes if their average glucose level is above 140 milligrams/dl Mean μ=147 Standard deviation σ=8 To determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured Once: Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula: Z=X-μσ Required probability is obtained as follows: PX¯>140=1-PX¯<140=1-PX¯-μσn<140-14781=1-PZ<-0.875=1-0.190787 [using Excel function "=NORM.S.DIST(-0.875,TRUE)"]=0.809213 (Or) using standard normal table, look up for z-value of -0.875 ≈-0.88 i.e., -0.8 in the row and .08 along the column, the intersection of both values gives a probability of 0.18943 Subtract the value from total probability 1, (since we want the area to the right of z-score and the table gives area to the left. ) That is, 1-0.18943=0.81057 Thus, probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured Once is 0.810 (b) To find the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured n = 2 times: Here, n = 2 Required probability is obtained as follows: PX¯>140=1-PX¯<140=1-PX¯-μσn<140-14782=1-PZ<-75.657=1-PZ<-1.24=1-0.10749 [using standard normal table]=0.89251 (c) To find the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured n = 4 times: Here, n = 4 Required probability is obtained as follows: PX¯>140=1-PX¯<140=1-PX¯-μσn<140-14784=1-PZ<-74=1-PZ<-1.75=1-0.04006 [using standard normal table]=0.95994 Using a standard normal table, look up for z value of -1.75 i.e., -1.7 in the row and .05 along the column, the intersection of both values gives a probability of 0.04006. Then subtract the value from total probability 1. Thus, required probability is 0.95994 Since, there are multiple subparts, we have solved first three parts for you. To get remaining subparts solved, please repost the complete question and mention the subparts to be solved.

Answered: A patient is classified as having…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ=147 mg/dl and σ=8 mg/dl, Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:
1. Once?

n=#+2 times, where # is the last digit of your student ID?
n=#+4 times, where # is the last digit of your student ID?
Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context.

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