What is the measurement of G?

What is the probability that a randomly selected member of a normally distributed population will lie more than 1.8 standard dev

Helen [10]

Answer:

$P(X> \mu +1.8\sigma)=P(\frac{X-\mu}{\sigma}>\frac{\mu +1.8\sigma-\mu}{\sigma})=P(Z>1.8)$

And we can find this probability using the complement rule:

$P(z>1.8)=1-P(z$

And using the normal standard distirbution table or excel we got:

$P(z>1.8)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable if interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sigma)$

We are interested on this probability

$P(X>\mu +1.8 \sigma)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X> \mu +1.8\sigma)=P(\frac{X-\mu}{\sigma}>\frac{\mu +1.8\sigma-\mu}{\sigma})=P(Z>1.8)$

And we can find this probability using the complement rule:

$P(z>1.8)=1-P(z$

And using the normal standard distirbution table or excel we got:

$P(z>1.8)=1-P(z$

5 0

4 years ago

An airliner maintaining a constant elevation of 2 miles passes over an airport at noon traveling 500 mi/hr due west. At 1:00 PM,

butalik [34]

Answer:

$\frac{ds}{dt}\approx 743.303\,\frac{mi}{h}$

Step-by-step explanation:

Let suppose that airliners travel at constant speed. The equations for travelled distance of each airplane with respect to origin are respectively:

First airplane

$r_{A} = 500\,\frac{mi}{h}\cdot t\\r_{B} = 550\,\frac{mi}{h}\cdot t$

Where t is the time measured in hours.

Since north and west are perpendicular to each other, the staight distance between airliners can modelled by means of the Pythagorean Theorem:

$s=\sqrt{r_{A}^{2}+r_{B}^{2}}$

Rate of change of such distance can be found by the deriving the expression in terms of time:

$\frac{ds}{dt}=\frac{r_{A}\cdot \frac{dr_{A}}{dt}+r_{B}\cdot \frac{dr_{B}}{dt}}{\sqrt{r_{A}^{2}+r_{B}^{2}} }$

Where $\frac{dr_{A}}{dt} = 500\,\frac{mi}{h}$ and $\frac{dr_{B}}{dt} = 550\,\frac{mi}{h}$ , respectively. Distances of each airliner at 2:30 PM are:

$r_{A}= (500\,\frac{mi}{h})\cdot (1.5\,h)\\r_{A} = 750\,mi$

$r_{B}=(550\,\frac{mi}{h} )\cdot (1.5\,h)\\r_{B} = 825\,mi$

The rate of change is:

$\frac{ds}{dt}=\frac{(750\,mi)\cdot (500\,\frac{mi}{h} )+(825\,mi)\cdot(550\,\frac{mi}{h})}{\sqrt{(750\,mi)^{2}+(825\,mi)^{2}} }$

$\frac{ds}{dt}\approx 743.303\,\frac{mi}{h}$

6 0

3 years ago

What is z 15 = -45+ z

damaskus [11]

Answer:

60 = z

Step-by-step explanation:

15 = - 45 + z

15 + 45 = z

60 = z

8 0

4 years ago

Y - X=-5<br> y = 2x2-3x-5<br> PLEASE HELP AND SHOW WORK <br> (substitution)

nikdorinn [45]

Answer:

Step-by-step explanation:

y - x = -5

y = x-5

y = 2x² - 3x - 5

x-5 = 2x² - 3x - 5

2x² - 4x = 0

x² - 2x = 0

x(x - 2) = 0

x = 2, 0

(x,y) = (2,-3), (0,-5)

8 0

3 years ago

1st answer will be brainliest

dsp73

1. 15*13=195
2. 7*13=91/2=45.5
3. 7*13=91/2=45.5

4. 195+45.5+45.5=286 units squared

hope this helps!

6 0

3 years ago