Mathematics, 02.07.2021 16:10 sjdswim

. It is known that the glucose level in blood of diabetic persons follows a normal distribution model with mean 106 mg/100 ml and standard deviation 8 mg/100 ml. a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml. b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?

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Answer from: burnsmykala23

a. 0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

b. 0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.

Step-by-step 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:

$Z = \frac{X - \mu}{\sigma}$

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.

Mean 106 mg/100 ml and standard deviation 8 mg/100 ml

This means that $\mu = 106, \sigma = 8$

a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

This is the p-value of Z when X = 120. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{120 - 106}{8}$

Z = 1.75

Z = 1.75 has a p-value of 0.9599

0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.

b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?

The proportion is the p-value of Z when X = 120 subtracted by the p-value of Z when X = 90. So

X = 120

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{120 - 106}{8}$

Z = 1.75

Z = 1.75 has a p-value of 0.9599

X = 90

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{120 - 106}{8}$

Z = -2

Z = -2 has a p-value of 0.0228

0.9599 - 0.0228 = 0.9371

0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.

Answer from: Quest

step-by-step explanation:

f(x)=2x^2 -1

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1

Answer from: Quest

x = 1

step-by-step explanation:

0 ÷ x = 0

0 ÷ 1 = 0