A person's blood glucose level and diabetes are closely...

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean ? = 90 and standard deviation ? = 27. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 140 (borderline diabetes starts at 140)

Transcript

00:01 A normal distribution is given for this question.

00:03 So the mean value, which is denoted by mood, this is equal to 90, and the standard deviation denoted by sigma, and that was equal to 27 here.

00:13 So we can define the random variable x, which is normally distributed.

00:17 This is, the mean is 90 and the standard deviation 27 here.

00:22 So what do we have to do for part a? we need to get the probability of the random variable x, which is more than means this is greater than 60.

00:29 In order to get this probability, i'm going to use the graphing display calculator application, which is a normal cdf, so the lower boundary is 60, there is no upper boundary with a very big number, and the mean is 90 in the standard division, 27 here.

00:42 Press second variance, and the second option, lower boundary and the upper boundary, sorry, this is upper boundary, and the mean is 90 in the standard division, which is 27.

00:57 So the probability would be how many decimal place, four decimal places, which is 0 .86 and 67.

01:05 And what about b? less than 110.

01:08 So x is less than 110.

01:11 Again, i'm going to use the normal cdf.

01:14 So the lower boundary.

01:17 The lower boundary here, which is negative 1e99, the upper boundary, 110, and the mean and the standard deviation.

01:27 Let me get the answer, press second variance.

01:29 The normal cdf here.

01:31 So the lower boundary, the upper boundary, and the mean is 90, and the standard division 207.

01:39 So the answer would be 0 .7 and 06.

01:43 And see which is between.

01:45 So the x is between 110 and greater than 60...

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