Answer:
0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large consignment of televisions contained 11% defectives.
This means that [tex]p = 0.11[/tex]
Sample of size 237
This means that [tex]n = 237[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.11[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.11*0.89}{237}} = 0.0203[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
P-value of Z when X = 0.11 + 0.03 = 0.14 subtracted by the p-value of Z when X = 0.11 - 0.03 = 0.08. So
X = 0.14
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.14 - 0.11}{0.0203}[/tex]
[tex]Z = 1.48[/tex]
[tex]Z = 1.48[/tex] has a p-value of 0.9306
X = 0.08
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.11}{0.0203}[/tex]
[tex]Z = -1.48[/tex]
[tex]Z = -1.48[/tex] has a p-value of 0.0694
0.9306 - 0.0694 = 0.8612
0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%
Suppose that the weights of airline passenger bags are normally distributed with a mean of 49.02 pounds and a standard deviation of 3.83 pounds. a) What is the probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds
Answer:
0.601 = 60.1% probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 49.02 pounds and a standard deviation of 3.83 pounds.
This means that [tex]\mu = 49.02, \sigma = 3.83[/tex]
What is the probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds?
This is the p-value of Z when X = 50. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 49.02}{3.83}[/tex]
[tex]Z = 0.256[/tex]
[tex]Z = 0.256[/tex] has a p-value of 0.601.
0.601 = 60.1% probability that the weight of a bag will be less than the maximum allowable weight of 50 pounds
What is the equation for a line that has an x-intercept of 2 and a y-intercept of -6?
Answer:
An x-intercept of 2 implies
(
2
,
0
)
is a point on the line
A y-intercept of 4 implies
(
0
,
4
)
is a point on a line
The slope of the line joining
(
2
,
0
)
and
(
0
,
4
)
is
#(Delta y)/(Delta x) = (4-0)/(0-2) = -2
Using the slope-intercept form of the equation
y
=
m
x
+
b
where
m
is the slope and
b
is the y-intercept
we have
y
=
−
2
x
+
4
Solve the equation
|x-3| -10=-5
Answer:
x=8 x=-2
Step-by-step explanation:
|x-3| -10=-5
Add 10 to each side
|x-3| -10+10=-5+10
|x-3| =5
Now separate into two equations , one positive and one negative
x-3 = 5 x-3 = -5
Add 3 to each side
x-3+3 = 5+3 x-3+3 = -5 +3
x=8 x=-2
Answer:
x = ± 8
Step-by-step explanation:
|x - 3| - 10 = - 5
|x - 3| - 10 + 10 = - 5 + 10
|x - 3| = 5
x - 3 = 5
x - 3 + 3 = 5 + 3
x + 3 = - 5
x + 3 - 3 = - 5 - 3
x = - 8
Using the proper terminology, how would you explain and visually demonstrate that this is not always the case.
Answer:
you drew to much on it
Step-by-step explanation:
What is the first step in evaluating the expression below?
12 + 6 - 4 : (2 + 5)
O Divide 4 by 2
O Add 2 and 5
O Add 12 and 6
O Subtract 4 from 6
Answer:
add two and five is the first step beacuse there in ()
Step-by-step explanation:
Answer:
Parentheses. Add 2 and 5.
Step-by-step explanation:
Use the P.E.M.D.A.S expression. (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.) As you can see, there are parentheses in your expression, so use PEMDAS to do order of operations problems like this.
5. Today, everything at a store is on sale. The store offers a 20% discount.
a. The regular price of a T-shirt is $18. What is the discount price?
b. If the regular price of an item is x dollars, what is the discount price in dollars?
C. The discount price of a hat is $18. What is the regular price?
Answer:
Step-by-step explanation:
20% = 20/100 = 0.2
The amount you need to pay for a T shirt is
Cost = original amount(100% - 20%)
Original amount = 18
100% - 20% = 80%
80% = 80 / 100 = 0.8
What this means is that you will pay 80% of the original cost.
Cost = 18*0.8
Cost = $14.40
Part B
Cost = 0.8 * x
Part C
Selling price = 0.8*Original Cost
Selling price = 18
18 = 0.8 * x
18/0.8 = x
x = 22.5
The original price was $22.50
Brenda has collected data to find that the finishing times for cyclists in a race has a normal distribution. What is the probability that a randomly selected race participant had a finishing time of greater than 154 minutes if the mean is 143 minutes and the standard deviation is 11 minutes? Use empirical rule. Provide final answer as a percent.
Answer: 16%
Step-by-step explanation:
Notice that 154 minutes is one standard deviation greater than the mean. Based on the empirical rule 68% of the finishing times are within one standard deviation of the mean, so 100%-68%=32% of the finishing times are outside of one standard deviation from the mean one either direction. Since the normal distribution is symmetric , half of the 32% will be less than the mean and half will be greater, so 16% of the finishing times are greater than the one standard deviation more than the mean.
The probability that race participant had a finishing time of greater than 154 minutes is 16%
The empirical rule states that for a normal distribution, 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are are within three standard deviation from the mean.
Given that mean (μ) = 143, standard deviation σ = 11
68% are within one standard deviation = μ ± σ = 143 ± 11 = (132, 154)The probability that race participant had a finishing time of greater than 154 minutes is 16% [(100% - 68%)/2]
Find out more at: brainly.com/question/12660012
The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?
Give the exact answer in simplest form.
____ square kilometers. (pi, fraction,)
Answer:
[tex]12.6\pi\:\mathrm{km^2}\:\text{or }\frac{63}{5}\pi\:\mathrm{km^2}[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] in degrees is given by [tex]r^2\pi\cdot\frac{\theta}{360}[/tex], where [tex]r[/tex] is the radius of the sector.
What we're given:
[tex]r[/tex] of 6[tex]\theta[/tex] of [tex]126^{\circ}[/tex]Substituting given values, we get:
[tex]A_{sec}=6^2\pi \cdot\frac{126}{360}=\boxed{12.6\pi\:\mathrm{km^2}}[/tex]
find the value of 4th terms by using 3n-2
Answer:
Step-by-step explanation:
[tex]4^{th} term \ means \ n = 4\\\\3n - 2 = 3 \times 4 - 2 = 12 -2 = 10[/tex]
Help with the slop for each one thanks
Answer:
13. zero slope
14. 1/2
15. undefined slope
16.-3/2 slope
3)
6 cm
5 cm
I
7 cm
5 cm
6 cm
Answer:
29
Step-by-step explanation:
in this sum, each letter stands for one of the digits 0 to 9
F O U R
+ O N E
= F I V E
can you replace the letters by digits to get s correct sum.( the first digit of a number cannot be zero so neither F nor O is zero)
Answer:
7 4 5 0
F O U R
+
4 8 1
O N E
=7 9 3 1
F I V E
Hope this is correct:)
Look at ZV SW and ZTSW in the image below.
Which of the following is the best description for this pair of angles?
O acute
O complementary
O straight
supplementary
Answer:
Supplementary is your answer
Điều kiện nf>=5;n(1-f)>=5 trong loại kiểm định giả thuyết " so sánh tỉ lệ tổng thể với số cho trước ", (với n là cỡ mẫu, f là tỉ lệ mẫu) có nghĩa là gì ?
Answer:
Step-by-step explanation:
which digit have the same place value and face value in 6782 1904
4 and 0 has the same place value and face value.
Hope this is helpful :)
Answer:
0 and 4 are the digit which have same place and face value.
In the diagram below, JK is similar to MNO. If segment Mn is 8 cm, segment Bo is 18 cm, segment OM is 20 cm, and segment JK is 22 cm, how long is segment LJ?
Answer:
55 cm
Step-by-step explanation:
[tex]\frac{22}{8} =\frac{x}{20} \\8x=440\\x=55cm[/tex]
Answer each question about the following arithmetic series:
12 + 18 + 24 + 30 + . . . + 198
What is the value of the arithmetic series?
630
1,260
3,360
6,336
Answer:
(c) 3360
Step-by-step explanation:
Given
The above arithmetic series where:
[tex]T_1 = 12[/tex] --- first term
[tex]d = 6[/tex] --- the common difference (18 - 12 = 6)
[tex]T_n = 198[/tex] --- The last term
Required
The value of the series
First, we calculate n using:
[tex]T_n = T_1 + (n - 1)d[/tex]
This gives:
[tex]198 = 12 + (n - 1)*6[/tex]
Collect like terms
[tex]198 - 12 = (n - 1)*6[/tex]
[tex]186 = (n - 1)*6[/tex]
Divide both sides by 6
[tex]31 = (n - 1)[/tex]
Make n the subject
[tex]n = 31 + 1[/tex]
[tex]n=32[/tex]
The sum of the series is:
[tex]S_n= \frac{n}{2}(T_1 + T_n)[/tex]
So, we have:
[tex]S_n= \frac{32}{2}(12 + 198)[/tex]
[tex]S_n= \frac{32}{2}*210[/tex]
[tex]S_n= 16*210[/tex]
[tex]S_n= 3360[/tex]
Use the variable x to write the phrase in symbols.
Answer:
155 + [tex]x^{3}[/tex] + 14
Step-by-step explanation:
The variable x would represent the number/value we don't know, and in this case, we don't know what number is raised to the third power. This being said, x would represent that number.
The question, although worded a bit confusingly, asks to add 155, the number (x) to the exponent of 3, and 14. Mathematically, this would be 155 + [tex]x^{3}[/tex] + 14.
Consider this linear function:
y= 1/2x+1.
Plot all ordered pairs for the values in the domain.
D: {-8, -4, 0, 2, 6}
Answer:
(-8,-3)
(-4,-1)
(0,1)
(2,2)
(6,4)
Step-by-step explanation:
One by one, substitue the x values and solve for y
Answer:
negative 4
Step-by-step explanation:
go
What is 10% of 14???
Answer: 1.4
Step-by-step explanation:
Answer: 1.4
Step-by-step explanation:
14 x 0.1 = 1.4
(10% = 10/10 0= 0.1)
HELP QUICK PLEASE 15 points!!!
Answer:
I think the ans is option 'a'
Final Answer:
Corresponding Angles Theorum; ∠AGF and ∠EHD are congruent
Can anyone solve this?
If square C is 64 in^2, then its dimensions are 8 x 8.
If square D is 81 in^2, then its dimensions are 9 x 9.
Since D is bigger than C and I sits in that extra space, then the dimensions of I are 1 x 1.
Since H is smaller than C, specifically I smaller, than its dimensions are 7 x 7.
Then, H and C make up one side of B, so 7 + 8 = 15. The dimensions of B are 15 x 15.
Since E is bigger than D by I, then the dimensions of E are 10 x 10.
If we find the length of the right side (B + C + D), which is 15 + 8 + 9 = 32, then we know that F + E + D must also add up to 32. F + 10 + 9 = 32 || F = 13. The dimensions of F are 13 x 13.
Then, F is E + G, so 13 = 10 + G. G = 3. The dimensions of G are 3 x 3.
Lastly, since we know the side length of the whole square is 32, then A + F must equal 32. 32 = A + 13. A = 19. The dimensions of A are 19 x 19.
A = 19 x 19 = 361 in^2
B = 15 x 15 = 225 in^2
C = 8 x 8 = 64 in^2
D = 9 x 9 = 81 in^2
E = 10 x 10 = 100 in^2
F = 13 x 13 = 169 in^2
G = 3 x 3 = 9 in^2
H = 7 x 7 = 49 in^2
I = 1 x 1 = 1 in^2
Hope this helps!! :)
Solve this equation 3-2.7(8-x)=16.5
Answer:
=13 :D
Step-by-step explanation:
Im bIg BrAiN
Answer:
x=13
Step-by-step explanation:
See image below:)
Please show process I WILL GIVE BRAINLY
Answer:
your image has the answer
Step-by-step explanation:
you can go type triangle calculator and type in everything
Help PLSSS!!!!! I will give brainlyest!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 17 1/2 or decimal form = 17.5
Step-by-step explanation: Hope this helped!
Answer:
17.5 Statues im pretty sure.
Step-by-step explanation:
7/8 divided by 1/20
PLEASE HELP ASAP !!!!!!!
Answer:
143º
Step-by-step explanation:
You want to find m<HBD
which is m<HBA minus m<BAD
180º minus 37º equals 143º
m<HBD is equal to 143º
Please give me brainliest
Can anyone who sees this answer my latest question?
I need help with it very soon.
Answer:
143 !
Step-by-step explanation:
URGENT.. pls help NO links
Answer:
.83
Step-by-step explanation:
we want
(sports∩Senior)/Senior
we can see that sports∩senior= 25
and senior= 25+5+5=30
25/30= .83
a city council consists of 7 democrats and 7 republicans. if a committee of 4 people is selected, find the probability of selecting 2 democrats and 2 republicans
Answer:
The probability of selecting 2 Democrats and 2 Republicans is 29.36%.
Step-by-step explanation:
Given that a city council consists of 7 democrats and 7 republicans, to determine, if a committee of 4 people is selected, the probability of selecting 2 Democrats and 2 Republicans must be performed the following calculation:
7/14 x 6/13 x 7/12 x 6/11 = X
0.5 x 0.46 x 0.58 x 0.54 = X
0.0734 = X
0.0734 x 100 = 7.34 x 4 = 29.36
Therefore, the probability of selecting 2 Democrats and 2 Republicans is 29.36%.
Evaluate + for x = 6, y=-4, and z=-2.
09
0 27
0-9
0-27
Answer:
-27
Hope this helped in anyway
Answer:
the answer to this is -27.
Which statement proves that this angle pair is the Corresponding Angles Theorem.
Criteria Laval
Answer:
its jess
here is ur ans
first option is your answer
• ANGLE 2 AND ANGLE 6 ARE CONGRUENT BECAUSE THEY ARE CORRESPONDING ANGLES.