Using the normal distribution and the central limit theorem, it is found that there is a 0.2119 = 21.19% probability that more than 77% of the sample have a driver's license.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem, we have that:
75% of high school seniors have a driver's license, hence p = 0.75.A sample of 300 is taken, hence n = 300.The conditions are verified because:
np = 300 x 0.75 = 225 > 10.
n(1-p) = 300 x 0.25 = 75 > 10.
The mean and the standard error are given by:
[tex]\mu = p = 0.75[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.75(0.25)}{300}} = 0.025[/tex]
The probability that more than 77% of the sample have a driver's license is one subtracted by the p-value of Z when X = 0.77, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{0.77 - 0.75}{0.025}[/tex]
Z = 0.8
Z = 0.8 has a p-value of 0.7881.
1 - 0.7881 = 0.2119.
0.2119 = 21.19% probability that more than 77% of the sample have a driver's license.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
(asin θ-bcos θ)²=?
[tex](a\sin(\theta) - b\cos(\theta))^2\\= a^2\sin^2(\theta) - 2ab\sin(\theta)\cos(\theta) + b^2\cos^2(\theta)\\= a^2\sin^2(\theta) - ab\sin(2\theta) + b^2\cos^2(\theta)[/tex]
Cups cost x dollars each. Mugs cost (x + 2) dollars each. (a) Write down an expression, in terms of x, for the total cost of 12 cups and 6 mugs. ............................................................................... dollars (2) (b) The total cost of 12 cups and 6 mugs is 57 dolllars.
work out the cost of 1 cup
Answer:
a. [tex]18x + 12[/tex]
b. $2.50
Step-by-step explanation:
a. If there are 12 cups and 6 mugs, and one cup is x and 1 mug is x+2, then multiply to get 18x + 12
b. Use the previous equation 18x+12=57 to get your answer. First move the 12 over to change the 57 to a 45. Then divide 45/18 to get 2.50 as you answer.
Which relation is a function?
Answer:
A
Step-by-step explanation:
A is the only one that has points that get hit only once when performing the vertical line test. All others get hit more than once per line.
PLEASE FASTTTT
FIND X AND Y PLEASEEE
Answer:
y = 2
x = -3.5
Step-by-step explanation:
3y and (2x + 13) are same-side angles.
that means they are equal
(that's not the real term for it, I just forgot what it's called)
using that, you can make this equation:
3y = 2x + 13
3y - 13 = 2x
(3y - 13)/2 = x
(5y - 4) and 3y are vertical angles.
vertical angles are equal.
using this, you can make the following equation:
5y - 4 = 3y
5y - 3y - 4 = 0
5y - 3y = 4
2y = 4
y = 2
now, substitute y for 2 in the original equation.
(3y - 13)/2 = x
(6 - 13)/2 = x
-7/2 = x
-3.5 = x
A farmer needs to purchase a rainwater harvesting tank and is deciding on the shape. He needs a tank that can hold at least 90 cubic feet of water. Select all the tanks that have a capacity of at least 90 cubic feet.
Answer:
Tank A and Tank D
Step-by-step explanation:
Got it right
The tanks that have the capacity more than 90 cu.ft is Tank A and C.
What is Volume?Volume is the amount of space occupied by a three dimensional object, it is represented in cubic units.
The volume of a Cylinder is given by
V = πr²h
The Volume of a Cone is given by
V= πr²h/3
The volume of the composite figure in Tank A and D,
Volume = Volume of cylinder + Volume of Cone
Tank A :
Volume = πr²h + πr²h/3
Volume = ( π * 2.5² * 4 ) + ( π *2.5² *2 )/3
Volume = 91.58 cu.ft
Tank B :
Volume = πr²h/3
Volume = π * 4² *5 /3
Volume = 83.7 cu.ft
Tank C
Volume = πr²h
Volume = π * 2² * 6
Volume = 75.36 cu.ft
Tank D:
Volume = πr²h + πr²h/3
Volume = π * 3²*3 + π *3²* 3 /3
Volume = 113.04 cu.ft
To know more about Volume
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32/w=4/12 on proportions on get more math
Answer:
w=96
Step-by-step explanation:
4x8= 32 so 12x8= 96 therefor it is 32/96
What is the length of PR?
A. 7
B. 8
C. 6
D. 9
Answer:
C
Step-by-step explanation:
The triangles are similar by the AA postulate, thus the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{AC}{PR}[/tex] , substitute values
[tex]\frac{20}{5}[/tex] = [tex]\frac{24}{PR}[/tex] ( cross- multiply )
20PR = 120 ( divide both sides by 20 )
PR = 6 → C
There are 14 boys and x girls in a class. One boy and one girl will be selected to represent the class on the student council.taylor says there are 152 different ways of chosing a boy and a gir l
2/5 part of the total number of students of a school are girls . If there are 240 boys, find the number of girls
Answer:
160 girls
Step-by-step explanation:
2/5 = girls
3/5 = boys
3/5 = 240
to find 1
240/3
80
2/5 = 160
PLESE ANSWER NUMBER 8 ASAP !!!!!
Answer:
the first one
Step-by-step explanation:
In the drawing below, QS bisects ZPQR,PO = 9 units, PS4 units, and RS-3 units.
What is OR in units?
O A 21
O B. 12
O C. 8
o D. 6 3/4
9514 1404 393
Answer:
D. 6 3/4
Step-by-step explanation:
The angle bisector divides the sides proportionally:
QR/PQ = RS/PS
QR = PQ×RS/PS = 9×3/4
QR = 6 3/4
Find the solutions to the equation 102x 11 = (x 6)2 – 2. which values are approximate solutions to the equation? select two answers. –9.6 –7.4 –4.6 –2.4 0.6
The approximate soluton of the equation 102x + 11 = (x + 6)² – 2 is 0.6. Then the correct option is E.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadratic equation is given below.
102x + 11 = (x + 6)² – 2
Open square, we have
102x + 11 = x² + 12x + 36 – 2
x² – 90x + 23 = 0
By the formula, we have the value of x
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{90 \pm \sqrt{(-90)^2}-4*1*23}{2*1}\\\\x = 89.74, 0.256[/tex]
The approximate soluton of the equation 102x + 11 = (x + 6)² – 2 is 0.6. Then the correct option is E.
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Answer:
A and D just did on edge
Step-by-step explanation:
Simplify this equation 8x-4+6x+15
Answer:
14x + 11
Step-by-step explanation:
Collect all the like terms together.
Positive 8x and positive 6x both have an x so after adding them together you get 14x. Negative 4 and positive 15 are also like terms so after adding them together you get positive 11.
The final answer being 14x + 11
Answer:
14x + 11
Step-by-step explanation:
8x - 4 + 6x + 15 =
8x + 6x + 15 - 414x + 15 - 414x + 11simplify this equation is 14x + 11
Working alone, it takes Chelsea 13 hours
to tar a roof. Ashley can tar the same roof
in 9 hours. How long would it take them
if they worked together?
Answer:
24 hours
Step-by-step explanation:
hoped this helped
What is the value of the expression below?
64^5/6
A) 10
B)56
C)32
D)2
Find the slope of the line that passes through (5, –6) has a y-intercept of –16.
Answer:2 I think
Step-by-step explanation:
(5,-6) (0,-16) -16- -6/0-5 = -10/-5 = 2
Simplify 7 + (−3).
PLEASE HELP!
Answer:
7-3=
10
Step-by-step explanation:
The positive sign is replaced by the negative sign.
+ve × -ve = -ve
What is the y-intercept for the equation y = 15x + 2?
Answer:
The y-intercept is +2
using y=mx+b we can tell anything added is the intercept.
+2
Step-by-step explanation:
We know the standard equation is
y = mx + c
where m is the slope and c is the y-intercept.
By Comparing the given equation with the standard equation we get,
y-intercept = +2
Hope it helps you!!A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $74. A season ski pass costs $350. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answer:
5 days
Step-by-step explanation:
On 5 days the daily pass would cost $495 while the season past would cost $475.
Dave wants to put a row of tiles in his kitchen.
The row has to be 3 m long.
Each tile is a square, with 25 cm sides.
How many tiles does he needs.
Answer:12 tiles will be needed.
Help!!!
x ≥ 4 if and only if 3x ≥ 12.
Answer: If 3x ≥ 12 then x ≥ 4 is true.
But x can be greater than or equal to 4 in other conditions:
4x ≥ 16
-3x ≤ -12
Step-by-step explanation:
Which table and graphs represents functions?
Answer:
Top Left, and Bottom Left
Step-by-step explanation:
A function cannot have the same y value for different x value
17 divivded by 5214 answer
Answer:
0.0032604526275412351361718450326
Step-by-step explanation:
17 divided by 5214 is 0.0032604526275412351361718450326
Hope I helped :)
Please consider Brainliest :)
Answer:
306.705882353
Step-by-step explanation:
(x + 5)(5 + x)
is this a perfect square
Answer:
NO this isn't a perfect square
Step-by-step explanation:
the diameter of a drum circle is 12 feet. what is the area of the drum
Answer:
37.68
Step-by-step explanation:
3.14 * 12 or 2(6 *3.14)
6 is the radius so you multiply by 2 and get 12. Multiply 12 by 3.14 to get 37.68
help me pls pls pls
nonsense=report
nice answer=brainles
pls dont waste my point
Answer:
27: 4 m
28: 60,000 cm
29: 8 m
30: 12 m
31: 90,000
32: 56 m
33: 650,000
34: 45 m
35: 230,000
36: 24
Have a great day!!
Please rate and mark brainliest!!
Answer:
Step-by-step explanation:
27. 4m²
28. 60 000cm²
29. 8m²
30. 12m²
31. 90 000cm²
32. 5.6m²
33. 650 000cm²
34. 45m²
35. 230 000cm²
36. 24m²
hope dis helps!!!!!
If f(x) = x + 2 and g(x) = 3x +4, then (g°f)(x) = ?
A) 3x +6
B) 3x +10
C) 3x² + 6x +4
D) 3x² - 10x +6
Answer:
B
Step-by-step explanation:
....Could you please HELP me....
Answer:
the answer is +4 because if you count it it is going up in fours
arlene begins a test with a possible total of 80 points. she loses 2 points every questions she answers incorrectly.
Answer: how many questions were incorrect? take that number and multiply it by 2. then subtract whatever u got from 80.
Step-by-step explanation:
1. R l : Z Y 2. R l : T Q 3. R l : B S 4. R m : S B 5. R l : F X 6. R l : S F
Answer:
look beloww
Step-by-step explanation:
could you please explain furture in a diffrent question so i can help?