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Shelia's measured glucose level one hour after a sugary drink varies according to the normal distribution with μ = 117 mg/dl and

TiliK225 [7]

Answer:

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

Step-by-step explanation:

To solve this problem, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 117, \sigma = 10.6, n = 6, s = \frac{10.6}{\sqrt{6}} = 4.33$

What is the level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L ?

This is the value of X when Z has a pvalue of 1-0.01 = 0.99. So X when Z = 2.33.

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

By the Central Limit Theorem

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

$2.33 = \frac{X - 117}{4.33}$

$X - 117 = 2.33*4.33$

$X = 127.1$

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

6 0

3 years ago

Describe the solution of the equation x^2+7x+2=0

yarga [219]

This is a quadratic equation with a general equation of ax^2 + bx + c.
The quadratic formula can help to get the roots of the equation. We know the highest degree of that equation is 2; so there will be also two roots.
The quadratic formula is
x = [-b ± √(b^2 - 4ac)] / 2a

With a = 1, b = 7, c = 2,
x = {-7 ± √[(7)^2 - 4(1)(2)]} / 2(1) = (-7 ± √41) / 2

So the two roots are
x1 = (-7 + √41) / 2 = -0.2984
x2 = (-7 - √41) / 2 = 0.2984

This is also another way of factorizing the equation
(x + 0.2984)(x + 0.2984) = x^2 + 7x + 2

4 0

2 years ago

Zzyzx Road is in California near Nevada. How many five-letter arrangements of the letters in the English alphabet follow Zzyzx a

Gemiola [76]

This problem can be solved using the concepts of permutation.

Zzyzx is the word. It has five letters. It asked as to how many five-letter arrangements of the letters in the English alphabet follow Zzyzx alphabetically.

Take note: <span>alphabetically
</span>
The two remaining five-letter after Zzyzx are Zzyzy and Zzyzz.
The remaining arrangements are of the form Zzz _ _.
There are 26 × 26 = 676 ways to fill in the last two letters, so following Zzyzx alphabetically, there are 2 + 676 = 678 arrangements.

7 0

3 years ago

The diameter of the circle above is 92 cm. What is the circumference of the circle? Use = 3.14

Mice21 [21]