Question

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 and standard deviation of What is the probability that, for an adult after a 12-hour fast, x is less than 104

Answer 1

The pvalue of Z when X = 104.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability that, for an adult after a 12-hour fast, x is less than 104?

This is the pvalue of Z when X = 104.

`Z = (X - \mu)/(\sigma)`

`Z = (104 - \mu)/(\sigma)`

`\mu` and
`\sigma` are the values of the mean and of the standard deviation, respectively.