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 $\mu$= 78 and standard deviation of $\sigma$= 25. What is the probability that, for an adult after a 12-hour fast, x is more than 49?
A)0.438
B)0.188
C)0.062
D)0.377
E)0.877

Question

Quizplus · Accepted Answer

To find the probability that x is more than 49, we use the normal distribution properties. First, calculate the z-score: $z = \frac{x - \mu}{\sigma} = \frac{49 - 78}{25} = -1.16$. Looking up this z-score in a standard normal distribution table or using a calculator gives the probability of being less than 49. To find the probability of being more than 49, subtract this value from 1. The result is approximately 0.877, indicating a high likelihood of x being more than 49 after a 12-hour fast.

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

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