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 of 74 and standard deviation of 29. What is the probability that, for an adult after a 12-hour fast, x is more than 37? haveing trouble with the formula and finding the answer, please help

Z = (score - mean)/SD

Z = (37-74)/29 = -1.28

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion for that Z score.

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 μ = 89 and standard deviation σ = 26. 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)

To find the probability that x is more than 37, we need to calculate the area under the normal distribution curve to the right of 37.

First, we need to standardize the value 37 using the z-score formula:

z = (x - μ) / σ

Where:
x = 37 (value we want to calculate the probability for)
μ = 74 (mean of the distribution)
σ = 29 (standard deviation of the distribution)

Plugging in the values, we get:

z = (37 - 74) / 29
z = -1.28

Now, we need to look up the probability associated with this z-value in the standard normal distribution table or use a calculator. The probability associated with a z-value of -1.28 is approximately 0.3997.

However, since we want to find the probability of x being more than 37, we need to calculate the area to the right of 37. This can be done by subtracting the probability of the z-value from 0.5:

P(X > 37) = 1 - P(Z < -1.28)
P(X > 37) = 1 - 0.3997
P(X > 37) ≈ 0.6003

Therefore, the probability that x is more than 37, for an adult after a 12-hour fast, is approximately 0.6003 or 60.03%.

To find the probability that x is more than 37, we need to calculate the probability of the event that x is greater than 37.

In order to do this, we require the z-score, which is a measure of how many standard deviations an observation or data point is from the mean. We can find the z-score using the formula:

z = (x - μ) / σ

Where:
- x is the value we want to find the probability for (37 in this case)
- μ is the mean of the distribution (74 in this case)
- σ is the standard deviation of the distribution (29 in this case)

Let's calculate the z-score:

z = (37 - 74) / 29
z = -1.27

Once we have the z-score, we can use a standard normal distribution table or calculator to determine the probability associated with this z-score.

The probability that x is more than 37 is equivalent to the probability that z is greater than -1.27. You would need to use the cumulative distribution function (CDF) of the standard normal distribution to find this probability.

Using a standard normal distribution table, the cumulative probability for z = -1.27 is approximately 0.1020.

Therefore, the probability that x is more than 37 is approximately 0.1020 or 10.20%.