Assume blood glucose levels in a population of adult women...

Assume blood-glucose levels in a population of adult women are normally distributed are normally distributed with mean 90 mg/dL and standard deviation 38 mg/dL. a. Suppose the "abnormal range" were defined to be glucose levels outside of 1 standard deviation of the mean (i.e., either at least 1 standard deviation above the mean, or at least 1 standard deviation below mean). Individuals with abnormal levels will be retested. What percentage of individuals would be called "abnormal" and need to be retested? what is the normal range of glucose levels in units of mg/dL? b. Suppose the abnormal range were defined to be glucose levels outside of 2 standard deviations of the mean. What percentage of individuals would now be called "abnormal"? What is the normal range of glucose levels (mg/dL)? c. In this the new study the experimental group, receiving a high carb diet has a mean of 133 mg/dL glucose. At a alpha of 5%, is there a difference between the control population and the experimental sample.

Transcript

00:01 Hello everyone so this is the question that we have we are assuming that blood glucose levels in a population of adult women in adult adult women are normally distributed with the mean value of 90 milligram by t f and a standard deviation standard deviation of 38.

00:42 So, i'll denote mean by mu and i'll denote standard deviation by sigma.

00:51 So now there are three parts of this question that suppose the abnormal range were defined to be clucose level outside of one standard deviation, abnormal, abnormal range is defined as outside of outside of outside of one standard deviation and of and of the mean.

01:23 So what percentage of the individuals would be called abnormal and needed to be tested? what percentage of others are abnormal and needs to be rested and what is the normal range of glucose level and now part b that suppose the abnormal range were defined to be glucose level outside of two standard deviation so abnormal range in part b is abnormal range outside outside outside two levels of standard deviation of the mean.

02:32 So again, abnormality and how many percentage needs to be rested.

02:38 So see, in this new study, the experimental group receiving a high carb diet, high carbide has has a mean of 133 millie gras tl glucose at an alpha of at an alpha of 5%.

03:04 So is there any difference i have to tell that is there any difference any difference between the control population and the experimental sample and the experimental sample now let's jump on to the solution of the question so let's solve part a first so that if the values are given to me with the mean value of this and this so i have to find that given normal distribution about 68 % of the observations lie in between observe 68 % of the observations lie in between so this is if i have 90 the mean value and standard deviation is 38 so 90 plus 38 so this would be mu minus sigma 1 value and mu plus sigma that is mean minus standard deviation and mean plus standard deviations are 90 minus 38 and 90 plus 38 so this would be equal to 52 comma 128 now let's jump on to part b part b about 95 % of the area under the normal curve within two standard deviation of the mean so this would be 95 % of the distribution lie in between...

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