Answer:
a. 0.6826 = 68.26% probability that a randomly selected x-value from the distribution is between 29 and 37.
b. 0.4987 = 49.87% probability that a randomly selected x-value from the distribution is between 33 and 45.
c. 0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at least 29.
d. 0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at most 37.
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 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.
A normal distribution has a mean of 33 and a standard deviation of 4.
This means that [tex]\mu = 33, \sigma = 4[/tex]
a. between 29 and 37
This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 29. So
X = 37
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{37 - 33}{4}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 29
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29 - 33}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability that a randomly selected x-value from the distribution is between 29 and 37.
b. between 33 and 45
pvalue of Z when X = 45 subtracted by the pvalue of Z when X = 33. So
X = 45
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 33}{4}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 33
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33 - 33}{4}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.9987 - 0.5 = 0.4987
0.4987 = 49.87% probability that a randomly selected x-value from the distribution is between 33 and 45.
c. at least 29
This is 1 subtracted by the pvalue of Z when X = 29. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{29 - 33}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
1 - 0.1587 = 0.8413
0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at least 29.
d. at most 37
This is the pvalue of Z when X = 37. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{37 - 33}{4}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at most 37.
Following are the solution to the given points:
Given:
[tex]\to Mean \ (\mu)= 33\\\\ \to \text{standard deviation}\ (\sigma) =4 \\\\[/tex]
To find:
find points=?
Solution:
For point a:
[tex]\to P (29 <x<37) = P(\frac{29-33}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{37-33}{4} )[/tex]
[tex]= P(\frac{-4}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{4}{4} )\\\\= P(-1 \leq z \leq 1 )\\\\= P(-1 < z <1 )\\\\= P(Z <+1) - P(Z <-1) \\\\=0.84134 - 0.15866\\\\= 0.68268 \\\\=68.268\%[/tex]
For point b:
[tex]\to P (33 <x<45) = P(\frac{33-33}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{45-33}{4} )[/tex]
[tex]= P(\frac{0}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{12}{4} )\\\\= P(\frac{0}{4} \leq \frac{X-\mu}{\sigma} \leq 3 )\\\\= P(-2< z< 0)\\\\= P(Z <-2) - P(Z <0) \\\\=0.9987-0.5 \\\\= 0.4987\\\\= 49.87\%[/tex]
For point c:
When X = 29, subtract by 1 from the p-value of Z.
Using formula:
[tex]\to Z = \frac{X -\mu}{\sigma}\\\\[/tex]
[tex]=\frac{29-33}{4} \\\\ =\frac{-4}{4} \\\\= -1 \\\\=1 - 0.1587 \\\\= 0.8413 \\\\= 84.13\%[/tex]
For point d:
[tex]\to Z = \frac{X -\mu}{\sigma}\\\\[/tex]
[tex]= \frac{37-33}{4}\\\\ =1\\\\ =\text{1 has a p-value of}\ 0.8413\\\\=0.8413 \\\\= 84.13\%[/tex]
So, the answer is " 68.268%,49.87%, and 84.13%"
Learn more about the normal distribution:
brainly.com/question/12421652
What is the approximate length of arc S on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth.
cuantos kilogramos
equivale la fracciom 11/25
Answer:
En español:
11/25 = 0.44
0.9702 porque multiplica por 2.205.
In English:
11/25 = 0.44
0.9702 because you multiply by 2.205.
the sum of -6 times a number x and 9 is at least 27. what are the possible values of the number
In the class legal case of Whitus v. Georgia, a jury pool of 90 people was supposed to be randomly selected from a population in which 27% were minorities. Among the 90 people se- lected, 7 were minorities. The baseline hypothesis, or null, was that the jury selection process was random. The test hypothesis, or alternative, was the process was not random (suggesting bias).
Find the probability of getting 7 or fewer minorities in a world where the jury pool selection pro- cess was supposed to be random.
a. .35400000
b. .00000354
C..00000451
d. 00000000
Answer:
C..00000451
Step-by-step explanation:
For each person in the jury, there are only two possible outcomes. Either they were minorities, or they were not. The probability of a person being a minority is independent of any other person. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Population in which 27% were minorities.
This means that [tex]p = 0.27[/tex]
90 people
This means that [tex]n = 90[/tex]
Find the probability of getting 7 or fewer minorities in a world where the jury pool selection pro- cess was supposed to be random.
This is
[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{90,0}.(0.27)^{0}.(0.73)^{90} \approx 0[/tex]
[tex]P(X = 1) = C_{90,1}.(0.27)^{1}.(0.73)^{89} \approx 0[/tex]
[tex]P(X = 2) = C_{90,2}.(0.27)^{2}.(0.73)^{88} \approx 0[/tex]
[tex]P(X = 3) = C_{90,3}.(0.27)^{3}.(0.73)^{87} = \approx 0[/tex]
[tex]P(X = 4) = C_{90,4}.(0.27)^{4}.(0.73)^{86} = 0.00000002[/tex]
[tex]P(X = 5) = C_{90,5}.(0.27)^{5}.(0.73)^{85} = 0.00000015[/tex]
[tex]P(X = 6) = C_{90,6}.(0.27)^{6}.(0.73)^{84} = 0.00000080[/tex]
[tex]P(X = 7) = C_{90,7}.(0.27)^{7}.(0.73)^{83} = 0.00000354[/tex]
So
[tex]P(X \leq 7) = 0.00000002 + 0.00000015 + 0.00000080 + 0.00000354 = 0.00000451[/tex]
So the correct answer is given by option C.
Pls help me guys!! :)
Answer:
what there is nothing, what can we help you
Answer:
I am ready to help you.ask question.
How could you correctly rewrite the equation 4(5 + 3) = 2(22 - 6) using the distributive property?
Answer:
We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.
4(5+3) = 2(22-6)
4(8) = 2(16)
32 = 32
Once you finish distributing each side, you can check to see if it is equal on both sides.
Step-by-step explanation:
Step-by-step explanation:
4(5 + 3) = 2(22 - 6)
4(8) = 2(16)
32 = 32
There are 12 inches in 1 foot. Jada is working on improving her vertical jump. She records the measurements in feet and inches. Currently, her standing reach is 6 feet from the ground. The highest point of her jump is 108 inches.
How many inches are in 6 feet?
6 feet = 72 inches.
Complete the statement to describe how to convert feet to inches.
To find the number of inches, ? the number of feet by the unit rate, ? inches per foot.
Answer:
To find out how any inches are in a certain amount of feet you have to multiply it by 12. For example 4 feet is equal to 48 inches. (4x12)
Step-by-step explanation:
1 Anthony purchased a car for $9,400. He paid 6.5% sales tax. How much tax did he pay?
Answer:
$8789
Step-by-step explanation:
you suptract 9,400. and 6.5%
Answer:
answer is $8789
Step-by-step explanation:
she is correct
5(8-70) + 29 nt (n=4
Answer:
5 x 8 = 40
5 x -70 = -350
40 - 350
29 x 4 = 116t
therefore it would be 40 - 350 + 116t
I think
In ANOP, the measure of P=90°, PN = 95 feet, and OP = 31 feet. Find the measure
of ZO to the nearest degree.
Answer: 72
Step-by-step explanation:
Geometry Need Help. I will give brainliest
Answer:
1 or 0.5
Step-by-step explanation:
What must the missing digit be so that the number rounds to 4 when rounding to the nearest whole number?
A. 5
B. 9
C. Any number greater than 5
D. The digit does not matter
Answer:
C. any number greater than 5
Step-by-step explanation:
when rounding numbers. 5 or more up the score. the number will be rounded to the next whole number
Answer:
Step-by-step explanation:
D the digit does not metter
The total surface area is _ square centimeters no freaking links bro
Answer:
180
Step-by-step explanation:
Find the area of each side by multiplying the length and width, times this answer by 2 since each face has another congruent face and then add them all up like (6*8*2)+(6*3*2)+(8*3*2)
Answer: Im most likely wrong since I suck at this stuff, but I think its 180
What is the equation of the horizontal asymptote?
A. y = 0
B. x = 0
C. y = x
D. x = 2
Answer:
horizontal asymptote at y = 0
Step-by-step explanation:
According to the definition of asymptotes, it is a line that the function gets closer and closer to as x goes to plus or minus infinity. The definition clearly does not mention anything about the finite value of x.
However, crossing of asymptotes does not happen in the case of vertical asymptotes because for a given x, the function has only one value but the same y can be obtained for different values of x.
It is a common misconception that graphs of functions can’t cross the asymptotes. This is true only for vertical asymptotes. In fact, there are several examples of functions whose graphs cross the horizontal asymptote. For example:
f(x) = (xe)^((-x)^2)
The horizontal asymptote of the above function is y=0 but it still crosses the x axis at x=0.
hope that helps, I really don't know thought. Quite tricky
Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. (Do not simplify.) Simplify the fraction from the previous step such that both the fractions have the common denominator The expression from the previous step then simplifies to using what? A. Addition and a Reciprocal Identity B. Addition and a Pythagorean Identity
Answer:
[tex](a)[/tex] [tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex](b)[/tex] [tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
(c) Addition and Quotient identity
Step-by-step explanation:
Given
[tex]\frac{2sec\theta}{csc\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex] --- The expression missing from the question
Solving (a): Write the left hand side in terms of sin and cosine
In trigonometry:
[tex]sec\theta = \frac{1}{cos\theta}[/tex]
and
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
So, the expression becomes:
[tex]\frac{2 * \frac{1}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{\frac{2}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Rewrite as:
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (b): Simplify
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Change / to *
[tex]\frac{2}{cos\theta}*\frac{sin\theta}{1} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (c): The property used
To do this, we need to further simplify
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Take LCM
[tex]\frac{2sin\theta+ 4sin\theta}{cos\theta} =6tan\theta[/tex]
Add the numerator
[tex]\frac{6sin\theta}{cos\theta} =6tan\theta[/tex]
Apply quotient identity
[tex]\frac{sin\theta}{cos\theta} = tan\theta[/tex]
This gives
[tex]\frac{6sin\theta}{cos\theta} = 6tan\theta[/tex]
Hence, the properties applied are:
Addition and Quotient identity
what is another way to show 2 x 4/6
Answer:
[tex]2 \frac{4}{6} [/tex]
I think this is it?? very sorry if it's incorrect
Answer:
4/3 or 1 1/3
Step-by-step explanation:
2 * 4/6
= 8/6 (You multiply 2 by the numerator, 4)
= 4/3 (Cancel out the common factor in the numerator and denominator, 2)
Mixed number form: 1 1/3
Let g(x)= - x^2 + 5x + 2, find and simplify g(-3)
Answer:
g(-3) = -4
Step-by-step explanation:
We are given the following function:
[tex]g(x) = -x^2 + 5x + 2[/tex]
Find and simplify g(-3)
We want to find the value of g when [tex]x = -3[/tex]. So
[tex]g(-3) = (-3)^2 + 5(-3) + 2 = 9 - 15 + 2 = -4[/tex]
g(-3) = -4
Yo this looks so confusing to me can someone answer this oraganized or sum
Answer:
2 units
Step-by-step explanation:
The x-coordinates are
School = 2
House = 5
Count the units (lines) between the two x-coordinates
There are 2 units between them
Biologists are interested in how temperature changes might affect the frequency of mating calls of frogs. Twenty gray tree frogs are randomly chosen for a study. For each frog, the temperature of its habitat (in degrees Celsius) and the frequency of its mating call (in tones per second) are recorded. The 96 percent confidence interval for estimating the population slope of the linear regression line predicting mating call frequency based on habitat temperature is given by 2.341±0.768. Assume that the conditions for inference for the slope of the regression line have been met. Which of the following is the correct interpretation of the calculated confidence interval?
a. We are 96 percent confident that the increase in mating call frequency of an individual frog when its habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
b. We are 96 percent confident that the average increase in mating call frequency in the sample of frogs when habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
c. We are 96 percent confident that the average increase in mating call frequency in the population of frogs when habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
d. We are 96 percent confident that the average increase in habitat temperature in the sample of frogs when mating call frequency increases by one tone per second is between 1.573 and 3.109 degrees Celsius.
e. We are 96 percent confident that the average increase in habitat temperature in the population of frogs when mating call frequency increases by one tone per second is between 1.573 and 3.109 degrees Celsius.
Answer:
c. We are 96 percent confident that the average increase in mating call frequency in the population of frogs when habitat temperature increases by 1 degree Celsius is between 1.573 and 3.109 tones per second.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
The 96 percent confidence interval for estimating the population slope of the linear regression line predicting mating call frequency based on habitat temperature is given by 2.341±0.768.
This means that the 96% CI is between:
2.341 - 0.768 = 1.573
2.341 + 0.768 = 3.109
Which of the following is the correct interpretation of the calculated confidence interval?
We are 96% sure that the population mean(population of frogs) in mating call frequency is in this interval. So the correct answer is given by option c.
WILL MARK BRAINLIST
The second story gutters of a house need to be cleaned. The gutters are 18.7 ft. high on the house. If a ladder will be placed 6 ft. from the base of the house, how long will the ladder need to be to reach the gutters? Round to the nearest foot. *
A. 18 ft
B. 19 ft
C. 20 ft
D. 21 ft
Answer:
C. 20 Ft.
Step-by-step explanation:
Using The Pythagorean Theorem, a²+b²=c² , insert the known variables into the equation.
18.7²+6²=c²
This gives you 385.69 + 36 = 385.69.
Next, square the result to find the missing side length.
[tex]\sqrt{385.69[/tex]
The answer comes out to around 19.6, which can be rounded up to 20ft.
Hope this helped!
Line segment AB has endpoints A(2,7) and B(6,5). Line segment CD has endpoints C(0,2) and D(4, -6). Part A: Determine the slope of AB and CD. Part B: Can line segments AB and CD be two opposite sides of a parallelogram? Explain your reasoning.
Answer:
slope of AB = -1/2
slope of CD = -2
No.
Step-by-step explanation:
slope of AB = (5-7)/(6-2) = -2/4=-1/2
slope of CD = (-6-2)/(4-0) = -8/4 =-2
for being two opposite sides of parallelogram, their slopes should be equal. But there slopes aren't equal
Please help
Chose of the problems a or b
Thank you!!
Answer:
a. x = 13m, b. x = 12cm
Step-by-step explanation:
a. x² = 12² + 5² (Pyth. theorem)
x = 13 m
b. 15² = 9² + x² (Pyth. theorem)
x = 12 cm
What is the equation for the line of reflection?
x=6
y=6
y=x
y=2
I need help with this plz help how do I do
Answer:
x ≤ 9 (Up to nine people)
Step-by-step explanation:
12 + x ≤ 21
x ≤ 9 (Subtracted both sides by 12)
Hope this helps! <3
I Need help plz will give brainlyist for the correct answer
help me this is the second time i have asked this 20 points
don't put something dum pls
Answer:
1. y=7x
2. y=9x
3. y=13x
4. x=10y
5. y=(x)*5+1
7. Draw a line through (0, 1) and (1, 6)
8. Draw a line through (0, 2) and (1, 3)
9. Draw a line through (0, 3) and (6, 1)
10. Draw a line through (0, 40) and (20, 80)
to 3 d.p.
9.
The head of the axe shown in figure 14.1 is a wedge of length 18.3 cm and
width 12 cm. It has a cylindrical hole of diameter 4 cm and its greatest
thickness is 6 cm. Find the volume of the metal used in making the axe.
18.3 cm
12 cm
6 cm
Fig. 14.1
Answer:
12 cm (I don't understand bro):(
In a survey of 140 undergraduate students in an elementary statistics class at UW, 12 said they were left-handed and 128 said they were right-handed. Assume the students are representative of all UW undergrads. Do these data provide evidence that the proportion of UW undergrads who are left-handed differs from the national proportion of 0.10 at the 5% significance level?
data: 12 out of 140, null probability 0.1 z = 0.563, p-value = 0.5731 alternative hypothesis: true p is not equal to 0.1 95 percent confidence interval: 0.04971124 0.14384532 sample estimates: P 0.08571429
a) Define the null and alternative hypothesis for answering the question being asked. Define both in words and in symbols.
b) The R output for running this test is shown below. What do you conclude for this test? Include your decision and an interpretation in the context of the problem. Be specific.
c) Explain in words what the p-value of 0.5731 means.
Answer:
a) The null hypothesis, H₀; p = 0.1
The alternative hypothesis, Hₐ; p ≠ 0.1
b) The proportion of left handed undergrads in UW differs from the national proportion of 0.1
c) The p-value is larger than the level of significance therefore there is statistical evidence supporting the alternative hypothesis
Step-by-step explanation:
The given data are;
The number of students in the sample, n = 140
The number of left handed students in the sample = 12
The number of right handed students in the sample = 128
The proportion of left handed students in the sample, [tex]\hat p[/tex] = 12/140 = 0.08571429
The significance level = 5%
The national proportion, p₀ = 0.1
a) The null hypothesis, H₀; p = 0.1
The null hypothesis is the proportion of left handed students in the UW is the same as the national proportion of 0.1
The alternative hypothesis, Hₐ; p ≠ 0.1
The alternative hypothesis is the proportion of left handed students in the UW is not the same as the national proportion of 0.1
b) Given from the output values of the Confidence Interval at 95% confidence level, (0.04971124, 0.14384532) which are both positive values, and the p-value of 0.5731, we conclude that there is a difference between the proportion of left-handed UW undergraduate students and the national proportion of 0.1
c) Given that the p-value of 0.5731 is larger than the significance level of 0.05, we reject the null hypothesis and there is significant statistical evidence to suggest that the proportion of UW undergrads who are left handed differs from the national proportion of 0.10
2 Write 3 x 10 in standard notation.
Answer:
30
Step-by-step explanation:
3 x 10 = 30
add the 0 from ten to 3 and you get 30
Solve for t.
4 (t + 1/4) = 3
Answer:
t=1/2
Step-by-step explanation: