Answer:
P ( X < 4 ) = 0.1736706
Step-by-step explanation:
Given:
- A random variable X follows a binomial distribution as follows,
Where n = 8, and p = 0.6.
Find:
- P ( X < 4 )?
Solution:
- The random variable X follows a binomial distribution as follows:
X ~ B ( 8 , 0.6 )
- The probability mass function for a binomial distribution is given as:
pmf = n^C_r ( p )^r (1-p)^(n-r)
- We are asked to find P ( X < 4 ) which is the sum of following probabilities:
P ( X < 4 ) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 )
- Use the pmf to compute the individual probabilities:
P ( X < 4 ) = 0.4^8 + 8^C_1*(0.6)*(0.4)^7 + 8^C_2*(0.6)^2*(0.4)^6 + 8^C_3*(0.6)^3*(0.4)^5 .
P ( X < 4 ) = 6.5536*10^-4 + 7.86432*10^-3 + 0.04128768 +0.12386304
Answer: P ( X < 4 ) = 0.1736706
One day, you go to a store and buy a pencil. It costs $0.25.
You notice the unit price $0.25/pencil.
The next day you buy 3 pencils, they cost $0.75.
You notice the unit price is $0.75/(3 pencils) = $0.25/pencil.
For each extra pencil you buy, the increase in price is always $0.25.
This suggests a linear relation between the number of pencils, p, and the cost of the pencils, c.
You use a linear equation to give you the cost of pencils based on the number of pencils.
c = 0.25p
One day, you happen to have $4.50 in your pocket.
You'd like to buy 15 pencils, but you are not sure you have enough money.
You use your handy linear equation, and you replace p, the number of pencils, with 15 to find their cost, c.
c = 0.25p
c = 0.25 * 15
c = 3.75
After using your equation, you see that 15 pencils cost $3.75, and since you have $4.50 you have enough money to buy them. You're very happy about this, and, as soon as you get home, you write this experience in your journal, using one of the new pencils you just bought, and you make it a point to include the linear equation that helped you.
If a > 1 then its s vertical stretch by a factor a.
If a < 1 its a compression
<u>Given</u>:
Line segment DM with end points D(-4,5) and M(6,0) is reflected about the x - axis to give line segment D'M'.
We need to determine the coordinates of the point D'.
<u>Coordinates of the point D':</u>
The general to reflect the coordinates over the x - axis is given by
To determine the coordinates of the point D', let us substitute the coordinates of the point D in the above rule.
Thus, we get;
The reflection of the coordinate D(-4,5) about the x - axis to give the point D' is (-4,-5)
Thus, the coordinates of the point D' is (-4,-5)
Answer:
The interger is up to 27
Step-by-step explanation:
let X represent the number of people.
For fewer than 28 people, we have;
(X ∠28)
Meaning,
(X ∠28) = (X ≤27)
(X = 1) + (X = 2) + (X = 3) ............+ (X = 27)
1 +1 + 1 +...............(27 times)
Therefore, the interger is up to 27