A person's level of blood glucose 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 $\mu$ = 71 and standard deviation of $\sigma$= 24. What is the probability that, for an adult after a 12-hour fast, x is between 35 and 110?
A)0.441
B)0.881
C)0.052
D)0.948
E)0.933

Question

Quizplus · Accepted Answer

To find the probability that x is between 35 and 110, we calculate the z-scores for 35 and 110 using the formula $ z = \frac{(x - \mu)}{\sigma} $. For x = 35, $ z = \frac{(35 - 71)}{24} = -1.5 $. For x = 110, $ z = \frac{(110 - 71)}{24} = 1.625 $. Using the standard normal distribution table, the probability for z = -1.5 is approximately 0.0668 and for z = 1.625 is approximately 0.9474. The probability that x is between 35 and 110 is 0.9474 - 0.0668 = 0.8806, which rounds to 0.881.

A Person's Level of Blood Glucose and Diabetes Are Closely μ\muμ

A Person's Level of Blood Glucose and Diabetes Are Closely $\mu$