jon started playing a computer game at 5:35 P.M. he finished the computer game at 5:52P.M How long did he play the game

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

zaharov [31]

Answer:

a) $P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

b) $P(X$

And we can find this probability uing the normal standard table:

$P(z$

c) $P(3.5$

And we can find this probability with this difference:

$P(-1.25$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.25$

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".

Part a

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

$X \sim N(5,1.2)$

Where $\mu=5$ and $\sigma=1.2$

We are interested on this probability

$P(X>3.5)$

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:

$P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

Part b

We are interested on this probability

$P(X$

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:

$P(X$

And we can find this probability uing the normal standard table:

$P(z$

Part c

$P(3.5$

And we can find this probability with this difference:

$P(-1.25$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.25$

3 0

2 years ago

Country A has a growth rate of 4.9% per year. The population is currently 4 comma 151,000, and the land area of Country A is 1

kvv77 [185]

Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

$P(t)=Pe^{rt}$

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one square yard of land.

So, there will be 14,000,000,000 person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

$\therefore 14,000,000,000= 151,000 e^{0.049t}$

$\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}$

Taking ln both sides

$\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|$

$\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|$

$\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}$

$\Rightarrow t}=1,892,147.588$ years

There will be one person for every square yard of land after 1,892,147.588 years.

7 0

3 years ago

The area of a circle is 78.5 cm² . Find the lenght of the radius of a circle . Use π = 3.14

Tpy6a [65]

Answer:

5cm = r

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

78.5 = 3.14 r^2

Divide each side by 3.14

78.5/ 3.14 = r^2

25 = r^2

Take the square root of each side

sqrt(25) = sqrt(r^2)

5 = r

6 0

2 years ago

Read 2 more answers

How do I 'Factor the expression 12p+30.' ?

s2008m [1.1K]

Answer:

Grouping and then use the common factor. Therefor the answer is 6(2p+5)

Step-by-step explanation:

I hope this helps.

5 0

2 years ago

Read 2 more answers

Help fast ASAP for 10 points

Zina [86]

Answer:

PQRS → P'Q'R'S'

Hope this helps you.

8 0

2 years ago

Read 2 more answers