Answer:
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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].
72% report that they color their hair to hide their gray.
This means that [tex]\mu = p = 0.72[/tex]
What is the probability that under 70% color their hair in a group of 85 older women?
For a sample of 85, we have that [tex]s = \sqrt{\frac{0.72*0.28}{85}} = 0.0487[/tex]
This probability is the pvalue of Z when X = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.7 - 0.72}{0.0487}[/tex]
[tex]Z = -0.41[/tex]
[tex]Z = -0.41[/tex] has a pvalue of 0.3409
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
Find angle Picture below
Answer:
14°
Step-by-step explanation:
Need 1 more brainliest
The TSA Is using an experimental computer to randomly select airline passengers for additional screening. Each person has a 0.7% chance of being selected. They test the new computer until 10 passengers are chosen for the additional screening, and then they remove it. Let the random variable be the number of passengers who pass through security until 10 are stopped for additional screening.
Is the number of passengers who pass through security in this time a binomial random variable?
Select all that apply
A. Yes. All four conditions are met.
B. No. There is not a fixed number of trials
C. No. The trials cannot reasonably be assumed to be independent.
D. No. The outcomes cannot be described as only "success" and-failure."
E. No. The probability of success is not the same for each trial
Answer:
B. No. There is not a fixed number of trials
Step-by-step explanation:
Binomial random variable:
Can only have two outcomes(yes/no questions).
Each trial must be independent, that is, the probability of a success is always the same in a trial, and the number of trials is fixed.
It's probabilities must be between 0 and 1.
Is the number of passengers who pass through security in this time a binomial random variable?
For each person, there are only two possible outcomes. Either they are screened, or not. However, we don't want to know the number of people screened, which is binomial, we want to know the number of people until 10 are screened, which is inverse binomial. So, since there is not a fixed number of trials, this is not binomial, and the answer is given by option B.
Can someone please help me !!
Answer:
A
Step-by-step explanation:
7 - (-7/5) x 5 =
7 - (-7) =
7 + 7 = 14
Hope that helps!
A line includes the points (–8, –2) and (–4, –3). What is its equation in slope-intercept form?
Answer:
y=mx+b
Step-by-step explanation:
m=slope
b=y-intersept
Calculate what is 365 {365- (365: (365+365)}}?
Step-by-step explanation:
365{365-(365:(365+365)}}
= 365{365-(365:730)}
= 365{365-0.5}
= 365{364.5}
= 133,042.5
ANSWER THEM PLEASEE I HAVE 20 MINSS
write the equation of a line that is parallel to y= 1/2x -4 and that passes through the point (9, -6)
Answer:
Step-by-step explanation:
y = ½x-4
slope of line is ½
slope of any parallel to the line is also ½
point-slope equation for line of slope ½ that passes through (9,-6):
y+6 = ½(x-9)
A local pizza place sends you online coupons. You can't combine the coupons and are trying to choose from two deals: $7.41 per medium two-topping pizza or 22% off the regular price of $11 for a medium two-topping pizza. Which deal is better and when?
Answer:
Step-by-step explanation:
W1
A pastry bag full of frosting forms a cone with the dimensions shown. Find the volume of frosting in the pastry bag.
Answer:
kajhfsdbbcbb,bnmcxbvljhhjw eutiugvawgygewfcufbuicmauigpuygpvghsfBgeilvlhkdb;bwgvPWIHITVNUAHUEIGEOYUGE8GPUWIEHOIgorucrugc t rueagurwWUGHCRWGCugpgpuyGPGCPGUGGUyguUYFUYGUOYUOYGOUYGOFUGIcefgyxsnjdfryugvouscbaknqpiuvhrwklemfnvvvvvvvr4uhui4jqkwserupwehdnjqhbgiwebduudirbgdqfwaiqjnweisdkrfmtguiwdnnnnnnnnnnnnnnerijjjjjjj
Step-by-step explanation:
Find all the zeros of the equation.
-x^3-x^2=11x+11
Answer:
x= -1 , i(sqrt11) , -i(sqrt11)
Step-by-step explanation:
subtract 11x from both sides
-x^3 - x^2 - 11x = 11
subtract 11 from both sides
-x^3 - x^2 - 11x - 11 = 0
Factor the left side of the equation
- (x - 1)(x^2 + 11) = 0
Set both factors to zero and solve for x
x + 1 = 0 x^2 + 11 = 0
-1 -11
x^2 = -11
x = -1 x = +/- i(sqrt11)
Find the prime factorization of 1,148 using a factor tree
Answer:
Prime Factors of 1148 = 2, 2, 7, 41
Which is the same as = 2² x 7 x 41
What is the solution of x = 2 + StartRoot x minus 2 EndRoot?
Answer:
x= 2 or x=3
Step-by-step explanation:
Both satisfy the equation. I hope this helped.
Answer:
x=2 or x=3
Step-by-step explanation:
just took the test it is C
Write the fraction as a product of a whole number and a unit fraction.
7/8
What's 2|–9| – |–2|? Question 14 options: A) –18 B) –20 C) 16 D) 20
16
find the absolute values ie. 9 and 2
multiply 9 by 2 and subtract 2 by 18
A dollar bill is 15.5 cm long and 6.5 cm wide. What is the area of
a dollar bill?
Answer:
I believe the answer is 100.75cm
5. 16^0 = * please i need help and i need the answer today not trying to rush but please thanx
Answer: 1
Step-by-step explanation:
16⁰ = 1
Anything to the power of zero is 1.
Smoking males in a given area have a mean life expectancy of 68.5 years, with a standard deviation of 5.3 years. The distribution of life expectancy is not assumed to be symmetric.
Between what two life expectancies does Chebyshev's Theorem guarantee that we will find at least 89% of smoking males?
Round your answers to the nearest tenth. Enter the bounds in ascending order.
Answer:
52.6, 84.4
Step-by-step explanation:
Chebyshev's Theorem guarantee that we will find at least 89% of smoking males in the life expectancy range [52.6, 84.4].
What is Chebyshev's inequality?In probability theory, Chebyshev’s inequality guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.
Let X be a random variable with mean μ with a finite variance σ², then for any real number k > 0, P(|X-μ| < kσ) ≥ 1-1/k².
Given,
Mean life expectancy = μ = 68.5 years
Standard deviation = σ = 5.3 years
P(|X-μ| < kσ) ≥ 1-1/k²
P(|X-68.5| < 5.3k) ≥ 1-1/k²
P(|X-68.5| < 5.3k) ≥ 0.89
[tex]1 - \frac{1}{k^{2} } = 0.89[/tex]
[tex]\frac{1}{k^{2} } = 0.11\\ \\\frac{1}{k^{2} } = \frac{1}{9} \\\\k = 3[/tex]
Between the following two life expectancies does Chebyshev's Theorem guarantee that we will find at least 89% of smoking males:
= [μ - 3σ, μ + 3σ]
= [68.5 - 3*5.3, 68.5 + 3*5.3]
= [52.6, 84.4]
Learn more about Chebyshev's inequality here
https://brainly.com/question/13184184
#SPJ2
Lily and Matthew are walking from home to school. Matthew has to return a library book on the way and follows the sidewalk. Lily walks directly to school. Assume the path they take forms a right triangle. Use the lengths in the diagram to determine how far Lily walks. Round your answer to the nearest tenth of a mile. Show your work and explain how you determined your answer. 20 points btw
Find angle picture below
Answer:
T=62
U=33
V=85
Step-by-step explanation:
Let (12,-5) be a point on the terminal side of an angle 0. Find the values of sin e, cose, and tan
Answer:
Sin = -5/13
Cos = 12/13
Tan = -5/12
Step-by-step explanation:
For the function N(y)=-3y-7, evaluate N(1)
Answer:
N(1) = -10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
N(y) = -3y - 7
N(1) is y = 1
Step 2: Evaluate
Substitute in y [Function]: N(1) = -3(1) - 7[Function] Multiply: N(1) = -3 - 7[Function] Subtract: N(1) = -10calcular
a. [1/3+4] =
b. [8-15+4]=
c. 4-√81/ √36=
Answer:
a. 1/7
b. -3
c. -50
Prove that
sinAtanA/1-cosA
= 1 + SECA
Answer:
The proof is done in the step-by-step explanation below.
Step-by-step explanation:
We are given the following identity:
[tex]\frac{\sin{A}\tan{A}}{1-\cos{A}}[/tex]
And we have to show that this is equals to:
[tex]1 + \sec{A}[/tex]
Multiplying numerator and denominator by the conjugate of the denominator:
[tex]\frac{\sin{A}\tan{A}}{1-\cos{A}} \times \frac{1+\cos{A}}{1+\cos{A}}[/tex]
[tex]\frac{\sin{A}\tan{A}(1+\cos{A})}{1 - \cos^2{A}}[/tex]
We use these following identities:
[tex]\sin^2{A} + \cos^2{A} = 1[/tex]
So
[tex]1 - \cos^2{A} = \sin^2{A}[/tex]
Also:
[tex]\tan{A} = \frac{\sin{A}}{\cos{A}}[/tex]
Then
[tex]\frac{\sin{A}\sin{A}(1+\cos{A})}{\cos{A}\sin^2{A}}[/tex]
[tex]\frac{\sin^2{A}(1+\cos{A})}{\cos{A}\sin^2{A}}[/tex]
[tex]\frac{1 + \cos{A}}{\cos{A}}[/tex]
[tex]\frac{1}{\cos{A}} + \frac{\cos{A}}{\cos{A}}[/tex]
[tex]\frac{1}{\cos{A}} + 1[/tex]
Since:
[tex]\sec{A} = \frac{1}{\cos{A}}[/tex]
We have that:
[tex]1 + \sec{A}[/tex]
Thus, the proof is done.
you are a beginner cyclist, so you typically ride at a speed of 12 miles per hour. your friend who has more experience and training with cycling rides at a speed of 16 miles per hour. one day you two decide to race, but because you are less experienced, your friend tells you that they will give you a three minute head start on the race.
how far can you ride before your friend catches up to you? write the system for this problem.
Answer:
Answer given below
Step-by-step explanation:
36, 48, 60....
16, 32, 48...
48 common in both.
Both will meet at 48 miles
So answer is 48 miles
a toy company is going to issue new ID codes to its employees.Each codes will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used. Assume that the digits can be repeated.. How many employee ID codes can be generated
Answer:
851,968
Step-by-step explanation:
26*8*8*8*8*8= 851,968
From the combination of codes, 851,968 employee ID codes can be generated.
Given,
Employee ID codes can be generated.
Each code will have one letter followed by five digits. The digits 2 and 6 will not be used. So, there are 26 letters and 8 digits that will be used.
The number of employee codes to be determined.
In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Required number of codes = 26 * 8 * 8 * 8 * 8 * 8
= 851,968
Thus, from the combination of codes, 851,968 employee ID codes can be generated.
Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ2
The graph of Fx), shown below, has the same shape as the graph of
G(x) = x, but it is shifted up 1 unit. What is its equation?
5+
F(x) =
Step-by-step explanation:
step 1. shifting f(x) up by one simply adds 1 to f(x).
step 2. if g(x) = x^2 then f(x) = x^2 + 1.
The equation of the function f(x) is f(x) = x²+1
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given is a function g(x) = x², and a function f(x) which have the same graph as the function g(x) = x², but it is shifted up 1 unit, we need to find the equation of the function f(x),
we are given that, it is shifted up 1 unit, that mean it has horizontal shift,
Rule for horizontal shift =
k(x) = k(x) + a [for upwards]
So, horizontal shift of 1 = g(x)+1
Therefore, f(x) = g(x)+1
or, f(x) = x²+1
Hence, the equation of the function f(x) is f(x) = x²+1
Learn more about functions, click;
https://brainly.com/question/12431044
#SPJ7
find the value of X.20,40,x
Step-by-step explanation:
267:(;»«=:3688865)):;(645789
which equation could have been used to create this table
Answer:
what table? there is no picture attached or answer choices.
Step-by-step explanation:
Lillian drew a design inside a circle.
Which measurement is closest to the
circumference of the circle?
F 25 cm H 50 cm
G 40 cm
J 32 cm
Answer:
H (50cm)
Step-by-step explanation:
Since 8 is the radius, 16 is the diameter. The formula for the circumference of a circle is diameter times pi, so 16pi is around 50
A deck of 40 cards contains 20 blue and 20 red cards. Each color has cards numbered 1 to 20.
Which events are independent? Choose all that apply.
Answer:
A red 5 is chosen from the deck. The card is put back into the deck and the a red card is chosen.
Step-by-step explanation:
An independent event is one whose outcome is not dependent on any other event. There are two types of cards in the deck. If a red card is selected it will be from the series 1 - 20, if the card is put back into deck and then again a red card is selected it will be again from the series 1 - 20. This is an independent event since its outcome is same irrespective of the events.
This is an independent event since its outcome is the same irrespective of the events.
What are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on the other.
If a variable is taking its values independently of any visible direct cause, then that variable is called an independent variable.
The variables that take their values based on some other variables' values are called dependent variables.
A deck of 40 cards contains 20 blue and 20 red cards. Each color has cards numbered 1 to 20.
This is an independent event since its outcome is the same irrespective of the events.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ5
