Please Help Fast!!! 20 points

A statistics practitioner determined that the mean and standard deviation of a data set were 120 and 30, is respectively. What c

BartSMP [9]

Answer:

a) 68% of the observations lie between 90 and 150.

b) 95% of the observations lie between 60 and 180.

c) 99.7% of the observations lie between 30 and 210.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Standard deviation = 120

Mean = 30

a. 90 and 150

This is within 1 standard deviation of the mean.

By the Empirical Rule, 68% of the observations lie between 90 and 150.

b. 60 and 180

This is within 2 standard deviations of the mean.

By the Empirical Rule, 95% of the observations lie between 60 and 180.

c. 30 and 210

This is within 3 standard deviations of the mean.

By the Empirical Rule, 99.7% of the observations lie between 30 and 210.

4 0

3 years ago

Plss help me TT

Marina CMI [18]

a. There are 0 or 2 real positive roots for the equation and

b. There are 0 or 2 real negative roots for the equation.

<h3>What is the Descartes'rule of sign?</h3>

Descartes' rule of sign states that

The number of real positive zero of a polynomial f(x) is the number of sign changes of the coefficients of f(x) or an even number less than the number of sign changes of the coefficients of f(x)
The number of real negative zero of a polynomial f(x) is the number of sign changes of the coefficients of f(-x) or an even number less than the number of sign changes of the coefficients of f(-x)

<h3>How to find the number of possible positive and negative roots are there for the equation?</h3>

Given the equation 0 = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1, writing it as a polynomial function, we have f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

<h3>a. The number of positive roots</h3>

So, to find the number of positive roots, we find the number of sign changes of the polynomial f(x).

So, f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, -2, + 8, -4, -1, there are two sign changes from -2 to + 8 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real positive roots.

So, there are 0 or 2 real positive roots for the equation.

<h3>b. The number of negative roots</h3>

So, to find the number of negative roots, we find the number of sign changes of the polynomial f(-x).

So, f(-x) = −8(-x)¹⁰ − 2(-x)⁷ + 8(-x)⁴ − 4(-x)² − 1

= −8x¹⁰ + 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, +2, + 8, -4, -1, there are two sign changes from -8 to + 2 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real negative roots.

So, there are 0 or 2 real negative roots for the equation.

So,

There are 0 or 2 real positive roots for the equation and
There are 0 or 2 real negative roots for the equation.

Learn more about Descartes' rule of sign here:

brainly.com/question/28487633

#SPJ1

8 0

2 years ago

The sum of angle V and angle W is 90 degrees. If cos W = 5/13, what is sin V? A. 5/13 B. 12/13 C.12/5 D. 13/5

Savatey [412]

Answer:

I think the answer to the question should be C

Step-by-step explanation:

3 0

3 years ago

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun

QveST [7]

Answer:

We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 31.7 milligrams

Sample mean, $\bar{x}$ = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s = 2.8 milligrams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}$

We use One-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429$

Now, $t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860$

Since,

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

3 0

3 years ago

Find the volume<br> Pls don’t answer if you don’t know the correct answer.

natulia [17]

can i just get a thank you ? lol

3 0

3 years ago