The mean is μ=140.
The standard deviation is σ = 6.4807.
The probability that X (number of successful treatments) is 128 or less is 0.0322.
What is normal distribution curve?In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.
According to the question,
An allergy medication is successful in treating 70%
The medication is given to 200 patients.
Thus,
The random variable X is a binomial random variable with n = 200 (there were 200 patients).
The probability that a medication is successful in treating a randomly selected patient is 0.7.
p = 0.7 (the medication was successful in 70% cases).
Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.
[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]
Substitute values of 'n' and 'p' to get the result,
[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]
Thus, the mean is obtained as 140.
The standard deviation is 6.4807.
Step 2: find P(X≤128)
As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.
[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]
[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]
Therefore, the probability that X is 128 or less. is 0.0322.
To know more about the normal distribution, here
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The complete question is-
An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.
A square cake sits on a circular cake stand. The circular cake stand has a diameter of 24 inches. The cake measures 16 inches on each side. How many square inches of the cake stand are visible?
Answer:
196.12 in^2
Step-by-step explanation:
circular cake stand area=(24/2)^2(3.14)=452.12 in^2
square cake=16x16=256 in^2
452.12-256=196.12 in^2
Select the correct answer.
Identify the vertex of the function graphed below.
A.
(0,-2)
B.
(3,1)
C.
(1,1)
D.
(2,2)
Answer:
I think the answer is B
Step-by-step explanation:
Answer:
think it d
Step-by-step explanation:
because when i pick (3,1) it was wrong so that why it think it D
Write the equation of the line that passes through the points (1,4) and (1,-3).
y = -7x+11
X=1
y = 7x - 3
Help If the side lengths of a cube are 16 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
16 ⋅ 3
16 ⋅ 16 ⋅ 16
163
316
Answer: I believe the answer is 6.3 I will research more and get a definite answer just dam me for the answer!
Step-by-step explanation:
:)
When someone throws a ball, the action force is the person pushing on the ball. What is the reaction force?
Give a real answer and explain.
Answer:
Should be : The Ball Pushing On The Person
Step-by-step explanation:
while the Air resistance answers have a point this question is asking about the reaction and the only reaction answer is the ball pushing on the person. every action has a reaction,
The ball wants to stay still so it pushes back on the person with all it's force, but the person pushes the ball with more force then the ball has so the ball rolls.
(may have explained it to much or weirdly sorry)
pls help me plssssss
Answer:
1
Step-by-step explanation:
It's the correct spelling.
At a certain store a half gallon jug of milk cost 2.95 and a gallon jug of milk costs 5.95. Which milk has cheaper price?
Answer:
The first milk
Step-by-step explanation:
2.95 × 2 = 5.90
The first milk has cheaper price.
Whos HAPPYYYYY today
Answer:
meeeeeeeeeeee super happy
-2(6) + 3(5 – 4· 2)
Answer:
-21
Step-by-step explanation:
Solve the inequality.
Step-by-step explanation:
subtract the value by placing it in the right side and multiply with 4.
Every time Kristina bakes a batch of brownies, she uses 1/8
a cup of chocolate. If she has 3/4
cup(s) of chocolate remaining, how many batches of brownies can Kristina make?
Answer:
6 batches
Step-by-step explanation:
3/4 divided by 1/8 = 6/8 divided by 1/8 = 6 batches
PROBLEM SOLVING A math club is having a bake sale. Find the area of the bake sale sign
TT IS
SWEET!
412ft
Math Club Baka Ina this Saturday
729 ft
The area of the sign is square feet.
The area of the bake sale sign is 6 ft²
Area
Area is the amount of space occupied by a two dimensional object.
Rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel.
The area of a rectangle = length * breadth
The area of the bake sale sign = length * breadth = [tex]\sqrt{4} *\sqrt[6]{729} = 6\ ft^2[/tex]
Find out more on Area at: https://brainly.com/question/25689052
Find the value of x in the following figure.
Answer:
x = 8
Step-by-step explanation:
180-(89+57)= 180-146 = 34
(5x -6) = 34
5x = 34 + 6
5x = 40
x = 40 ÷ 5
x = 8
help????????????????????
Answer:
x=11
Step-by-step explanation:
12x+2 and 2x+112 are opposite exterior angles so they are congruent
Answer:
x=11
Step-by-step explanation:
12x + 2 and 2x + 112 are vertical angles meaning that they are equal to each other so we set up an equation that says 12x + 2 = 2x + 112 and solve for x
12x+2=2x+112
step one subtract 2 from each side
12x=2x+112
step 2 subtract 2x From each side
10x=110
step three divide each side by 10
x=11
Número de departamento vendidos en un edificio cualitativa o cuantitativa.
Answer:The nucleus / large central vacuole contains
genetic material of a eukaryotic cell.
Step-by-step explanation:The nucleus / large central vacuole contains
Find the equation of the line which passes through (0,8) and (1,12)
Answer:y =4x + 8
Step-by-step explanation:
X-0/0-1 = y-8/8-12
Or,-4x = -y +8
So, y-4x = 8
Find the midpoint of the line segment from (4,5) to (-4,4)
9514 1404 393
Answer:
(0, 4.5)
Step-by-step explanation:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
((4, 5) +(-4, 4))/2 = (4-4, 5+4)/2 = (0, 9)/2 = (0, 4.5)\
The midpoint is (0, 4.5).
what is 40% of 10? PLZ HELP ASAP
Answer:
4
Step-by-step explanation:
10 * 40%
10 * 0.4 = 4
Answer:
Hi! 40% of 10=4
Step-by-step explanation:
Hope this helps! :)
Have a nice day! ♥
Can someone solve this for me?
2x + 7y = 4
( u have to put it in y = mx + b)
* but when i divide i get y = -2/7x + 4/7
is the 4/7 correct?
like r u allowed to have two fractions?
Answer:
I think that is correct because I got the same answer
Help me PLEASE! I will give Brainliest to the first correct answer.
Jada’s dog was 5 and 1/2 inches tall when it was a puppy. Now her dog is 14 and 1/2 inches taller than that. How tall is Jada’s dog now?
Answer:
20 inches tall
Step-by-step explanation:
First, I did 1/2+1/2=1. Then, I did 5+14=19. So, 19+1=20.
Solve each inequality for the variable. Show your work. 3x-7>4x+2
Step-by-step explanation:
3x-4x>2+7
-x>9
x>-9
Plz mark me as a brainlist
The six sided of number cube are labeled 1,2,3,4,5 and 6. You flip a coin and roll the number cube. What is the theoretical probability that the coin lands on heads and roll a number greater than 2?
heads = 1/2
>2 = 2/3
2/3 x 1/2 = 1/3
Answer:
1 / 3there is a line whose y-intercept is 10 and whose slope is -1/2. what is its equation in slope-intercept form? y= x +
Which properties justify the steps taken to solve the system? {2a+7b=03a−5b=31 10a+35b=0; 21a−35b=217 31a = 217 a = 7 2(7)+7b=0 14 + 7b = 0 7b=−14 b=−2 what are each of the steps taken?
9514 1404 393
Explanation:
2a+7b=0 . . . . . . . . given [eq1]
3a−5b=31 . . . . . . . .given [eq2]
10a+35b=0 . . . . . . multiplication property of equality 5×[eq1] = [eq3]
21a−35b=217 . . . . .multiplication property of equality 7×[eq2] = [eq4]
31a = 217 . . . . . . . . addition/substitution properties of equality [eq3]+[eq4]
a = 7 . . . . . . . . . . . . division property of equality (÷31)
2(7)+7b=0 . . . . . . . .substitution property of equality; a=7 in [eq1]
14 + 7b = 0 . . . . . . . properties of real numbers
7b=−14 . . . . . . . . . . addition property of equality; add -14
b=−2 . . . . . . . . . . . . division property of equality (÷7)
Can someone help me on this is for today pls!!!
Answer:
C
Step-by-step explanation:
The answer must be in square inches, not inches, so a and b are automatically wrong.
Couple of ways of doing it - the large triangles are congruent, so the area of each is the same. Since the area of a triangle is 1/2 base times height, the area of the 2 large triangles is just base times height, which is 18 * 11 or 198
Same principle for the smaller triangles at the top, area is 8 times 11, or 88. Add them up, you get 286 sq inches.
y=3x+−7
Find the slope.
A. 7
B. -7
C. 3x
D. 3
Answer:
D.3
Step-by-step explanation:
In the equation for a line in the form y=mx+c, m represents the slope.
Therefore the slope is 3.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + - 7 ← is in slope- intercept form
with slope m = 3
The question is in the picture
Answer:
(8, - 7)
Step-by-step explanation:
Since, (8, 7) is reflecting over x-axis, so after reflection, x- coordinate will remain same and y-coordinate changes from 7 to -7.
Therefore,
[tex] J(8,\: 7) \rightarrow J'(8,\: - 7)[/tex]
Answer:
-8,7 is the ans of the question
Here is an inequality: -x > 18. List some values for x that would make this inequality true.
Answer:
some examples x could equal:
x = -19
x = -20
x = -50
x = -100
so on
Step-by-step explanation:
remember negative x negative = positive
so any negative value beneath -18 will satisfy this because it will turn positive when multiplied by that outer minus sign.
hope this helped
There are (2^6)^3• 2^0bacteria in a sample. What is the total number of bacteria in the sample?
Answer:
262,144
Step-by-step explanation:
2^0 = 1
(2^6)^3 = 2^18 = 262,144
Answer: 262,144.
Step-by-step explanation: (26)3(20)
=(643)(20)
=262144(20)
=(262144)(1)
=262144
What is the slope of the line that passes through these two points (15,20) and (20,25)
Answer:
The slope Is 1.
Step-by-step explanation:
If you graph the two points it shows that the graph is done.
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (15, 20) and (x₂, y₂ ) = (20, 25)
m = [tex]\frac{25-20}{20-15}[/tex] = [tex]\frac{5}{5}[/tex] = 1