need with bell shape curve that shows are shaded and weve been doing the square root and sample distribution with them **Glucose Testing**Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both... In a test to screen for gestational diabetes, a patient is classified as needing further testing if the glucose level is above 130 milligrams per deciliter (mg/dL) one hour after consuming a sugary drink. Shelia’s measured glucose level follows a normal distribution with a mean (μ) of 122 mg/dL and a standard deviation (σ) of 12 mg/dL.(a) If a single glucose measurement is made, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?(b) If measurements are made on four separate days and the mean result is compared with the criterion of 130 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

Let X denote the Glucose level Then X~N(122, 122) According to the given information, further…

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need with bell shape curve that shows are shaded and weve been doing the square root and sample distribution with them

**Glucose Testing**

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both...

In a test to screen for gestational diabetes, a patient is classified as needing further testing if the glucose level is above 130 milligrams per deciliter (mg/dL) one hour after consuming a sugary drink. Shelia’s measured glucose level follows a normal distribution with a mean (μ) of 122 mg/dL and a standard deviation (σ) of 12 mg/dL.

(a) If a single glucose measurement is made, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

(b) If measurements are made on four separate days and the mean result is compared with the criterion of 130 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

Expert Solution

Step 1

Let X denote the Glucose level

Then X~N(122, 12²)

According to the given information, further testing is needed if the glucose level is greater than 130.

Part 1: Required probability is

$P (X \geq 130) = P (\frac{X - μ}{σ} \geq \frac{130 - μ}{σ}) = P (Z \geq \frac{130 - 122}{12}) = P (Z \geq 0.67) = 1 - P (Z \leq 0.67) = 1 - 0.75 = 0.25$

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