A fair coin is flipped four times. What is the probability of getting heads at least once?

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

Arnie decides to make 3 cups of dark orange paint and 3 cups of light orange paint.

dimulka [17.4K]

The question is an illustration of equivalent ratios.

3 cups of dark orange require 3 ounces of yellow paint
3 cups of light orange require 19.5 ounces of yellow paint

1 cup of dark orange requires

$Red = 7oz$

$Yellow =1oz$

To make 3 cups, we simply multiply by 3, because $3 \times 1 = 3$

So, we have:

$Red = 7oz \times 3 = 21oz$

$Yellow =1oz \times 3 = 3oz$

2 cups of light orange require

$Red =3oz$

$Yellow =13$

To make 3 cups, we simply multiply by 1.5, because $2 \times 1.5 = 3$

So, we have:

$Red = 3oz \times 1.5 = 4.5oz$

$Yellow = 13oz \times 1.5 = 19.5oz$

Hence:

3 cups of dark orange require 3 ounces of yellow paint
3 cups of light orange require 19.5 ounces of yellow paint

Read more about equivalent ratios at:

brainly.com/question/18441891

5 0

2 years ago

Jacob earned 300 on an amount deposited into his bank account for 3 years at a 2% annual simple interest rate how much did Joe d

vampirchik [111]

Joe deposited 180.

300 x .02 x 3 = 180

3 0

2 years ago

Find the unknown length y in the following pair of the similar triangles.

yulyashka [42]

Answer:

y = 9.75

Step-by-step explanation:

Since both triangles are said to be similar, the proportion or ratio of the sides of both triangles would be equal.

Therefore, 39/y = 23/5.75 = 35/8.75

Let's find y

39/y = 23/5.75

==>Cross multiply

39*5.75 = 23*y

224.25 = 23y

==>Divide both sides by 23

224.25/23 = y

9.75 = y

y = 9.75

Check:

Thus,

39/9.75 = 23/5.75 = 35/8.75 = 4

Our answer y, which is 9.75, is correct.

5 0

3 years ago

I help I’ve been stuck on this one

nlexa [21]

$202 + 156 = 358$
$500 - 358 = 142$
the answer is A. 142

7 0

2 years ago