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%"
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The length of stay at a specific emergency department in Phoenix, Arizona, in 2009 had a mean of 4.6 hours with a standard deviation of 2.9. Assume that the length of stay is normally distributed.
a. What is the probability of a length of stay greater than 10 hours?
b. What length of stay is exceeded by 25% of the visits?
c. From the normally distributed model, what is the probability of a length of stay less than 0 hours? Comment on the normally distributed assumption in this example.
Answer:
a) the probability of a length of stay greater than 10 hours is 0.03144
b) the length of stay is exceeded by 25% of the visits is 6.5 hrs
c)
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
Step-by-step explanation:
Given that;
mean μ = 4.6
standard deviation σ = 2.9
let x represent length of stay;
a. What is the probability of a length of stay greater than 10 hours?
p( x > 10 ) = p( x-μ/σ > 10-4.6 / 2.9 )
= p( Z > 1.86)
= P( Z < - 1.86 )
FROM THE Z SCORE TABLE;( Z < - 1.86 ) = 0.03144
p( x > 10 ) = 0.03144
Therefore, the probability of a length of stay greater than 10 hours is 0.03144
b) What length of stay is exceeded by 25% of the visits?
p( X > x ) = 0.25
so
p( X < x ) = 0.75
p( x-μ/σ < x-4.6 / 2.9 ) = 75
p( Z < x-4.6 / 2.9 ) = 0.75 ----- 1
also, from the standard normal table; P( Z < 0.67 ) = 0.75 ------ 11
from equation 1 and 11
x-4.6 / 2.9 = 0.67
x-4.6 = 2.9 × 0.67
x - 4.6 = 1.943
x = 4.6 + 1.943
x = 6.543 ≈ 6.5
Therefore, the length of stay is exceeded by 25% of the visits is 6.5 hrs
c) From the normally distributed model, what is the probability of a length of stay less than 0 hours?
P( X < 0 ) = p( x-μ/σ < 0-4.6 / 2.9 )
= P( Z - 1.59)
from table;( Z - 1.59) = 0.0559
P( X < 0 ) = 0.0559
The probability of length of stay less than 0 hours is 0.0559, length of stay cannot be less than 0. When the normal model is used, we assume that the LOF is approximately normally distributed.
The LOF is better modeled by the normal distribution near the mean and worse in the tails.
The probabilities in the left tail for the vales of X < 0 can be neglected.
What note receives one beat in 2/4?
Expand the following up to the term x⁴.
(2 + x)^-1
Answer:
Rewrite the expression using the negative exponent rule
rule b^-1 = 1/bn
1/2+x
Step-by-step explanation:
this is the correct answer you want.
A 10-foot ladder is leaning against a tree. The bottom of the ladder is 6 feet away from the bottom of the tree. About how high up the tree does the top of the ladder reach?
4 feet
6 feet
8 feet
16 feet
Answer:
8 feet
Step-by-step explanation:
Ladder = hypotenuse
bottom of ladder to tree = leg
x, 6, 10
Clear 3-4-5 triangle so,
x=8
-(3x + 1) > -7+3x
Plz help with this
Answer:
x<1
Step-by-step explanation:
Treat it like a normal equation
Distribute: -3x-1>-7+3x
Isolate x: -6x>-7+1
Because we are dividing by a negative number, we need to flip the sign
x<1
Answer:
0, -1
Step-by-step explanation:
1. Plug in for 5:
-(15 + 1) > -7 + 15
-16 > 8 (FALSE)
2. Plug in for 1
-(3 + 1) > -7 + 3
-4 > -4 (FALSE, they are equal)
3. Plug in for 0
-(0 + 1) > -7 + 3(0)
-1 > -7 (TRUE)
4. Plug in for -1
-(-3 + 1) > -7 - 3
-(-2) > -10
2 > -10 (TRUE)
5. Plug in for 20
-(60 + 1) > -7 + 60
-66 > 53 (FALSE)
6. Plug in for -32
-(96 + 1) > -7 + 96
-97 > 89 (FALSE)
You can find the answer by just plugging in for x. It's very easy and the rest is just addition and multiplication, so please put some effort. Hope this helps! :)
Lei is icing some cupcakes. She has 3/4 cups of frosting. Each cupcake needs 3/16 cup of frosting. How many can she frost?
Answer:
4
Step-by-step explanation:
3/4÷3/16
3/4×16/3
3•16=48
4×3=12
48÷12=4
Consider triangle ABC as pictured below. If B is transformed according to the rule (x,y) --> (x-4,y), then △AB'C will be a _______
Answer:
Right triangle
Step-by-step explanation:
7^2 + 6^2 = c^2
49 + 36 = c^2
85 = c^2
c = 9.22
Is this sample biased?
Answer:
No, this sample is not biased.
Step-by-step explanation:
Everyone in the grocery store has a fair chance of getting picked for the survey.
I hope this helped!! :3
Which shows a rational number plotted correctly on a number line?
Answer:
none of the 3 showing are correct
Step-by-step explanation:
Answer:
Pretty sure its A hope it helps! But i have to get back to my test .
Step-by-step explanation:
Help please I give brainliest and be serious
Answer:
you add all sides then you can calculate
y = 3x - 4; (2,7)
Write an equation for the line that is parallel to the given line and that contains the given point
Please help ASAP thank you
One, no, or infinitely many solutions?
Answer:
One solution
x = 3
Step-by-step explanation:
3x + 5 + 6x - 7 = 25
combine like terms:
9x -2 = 25
add 2 to each side of the equation:
9x = 27
divide both sides by n9:
x = 3
Branliest to correct answer please explain how you solved it
Answer: it is a.
Step-by-step explanation: because I'm smart.
Answer: 2% or 3%
Most likely 2%.
Step-by-step explanation:
There’s a 20 sided dice and 100÷20=5
but you have to think of it as 26
2% x 26= 0.52 make 0.52 a 52 and take off the 2 from 52 and make it your answer, 2%
thats what I came up with and gathered after some tests on a normal online calculator that doesn‘t do remainders.
The diameter of a circle is 3 meters. What is the circumference?
Answer:
C≈9.42m
Using any of this formulas
C=2πr
C=2πrd=2r
Solution:
C=πd=π·3≈9.42478m
Help plzzzzzzzzhwhehdhd
Answer: d, eight and fifty-three thousandths
Step-by-step explanation:
The number before the decimal place in the units column is a whole number (8).
The numbers after (.053) are thousandths because the whole number (8.053) consists of 4 numbers the same way a 1000 does.
Sorry I found the last bit harder to put into words, but I hope it helps :)
HELP PLEASE BRAINLYIST
Examine the diagram. It is not drawn to scale.
Wh at is the m angle 3?
Х
m angle 3=
Answer:
isn't it just 50°
Step-by-step explanation:
180=a straight line.
you are given 75° and 55°
75+55=130
180-130
Answer:
105
Step-by-step explanation:
Chupapi
Some loser deleted my answers
That's why it says 1 answer and 1.5k people helped
A farmer knows that a grocery store will reject a shipment of his vegetables if more than 4% of the vegetables contain blemishes. He inspects a large truckload of tomatoes to determine if the proportion with blemishes (p) exceeds 0.04. He selects an SRS of 150 tomatoes from the more than 2,000 tomatoes in the truck. Suppose that 8 tomatoes sampled are found to have blemishes. Which of the assumptions for inference about a proportion is violated, if any?
a. Large Counts: np > 10
b. Large Counts: n(1 – p) > 10
c. The sample is a random sample of the entire population.
d. 10% condition: the sample size is less than 10% of the population.
e. There do not appear to be any violations.
Answer:
Assumption A is violated
Step-by-step explanation:
x = number of blemishes = 8
n = sample size = 150
proportion = x/n = 8/150 = 0.0533
1. large counts: np> 10
= 150 * 0.0533 >10
= 7.995 > 10
this assumpton is obviously violated. 7.995 is not greater than 10
2. Large Counts: n(1 - p) > 10
150(1-0.0533)>10
150-7.995 > 10
142.005> 10
there is no violation. The assumption is satisfied
3. This assumption is satisfied. this is because the tomatoes were selected using simple random sampling.
4. 10% of the population = 0.1 * 2000 = 200
the sample size = 150
150 < 200
this assumption is satisfied
solve for x in the equation 5x-4=2x+20
The solution to the equation 5x - 4 = 2x + 20 is x = 8 which can be determined by simplification process.
To solve for x in the equation 5x - 4 = 2x + 20, we can follow these steps:
Start by isolating the x terms on one side of the equation. We can do this by subtracting 2x from both sides:
(5x - 2x) - 4 = (2x - 2x) + 20]
Simplifying:
3x - 4 = 20
Next, isolate the constant term on the opposite side of the equation by adding 4 to both sides:
(3x - 4) + 4 = 20 + 4
Simplifying:
3x = 24
Finally, solve for x by dividing both sides of the equation by 3:
(3x)/3 = 24/3
Simplifying:
x = 8
Therefore, the solution to the equation 5x - 4 = 2x + 20 is x = 8.
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Full Question-
Solve for x in the given equation 5x-4 = 2x+20
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
(-3,1) and (-8,6)
Step-by-step explanation:
Hey gabymcarrillo!
The solution is always the place where the two lines intersect.
Our first answer: go 3 left on the x- axis, and then go 1 up on the y- axis. This results in (-3,1)
Our second answer: go 8 left on the x- axis, then go 6 up on the y- axis. This results in (-8,6)
Hope a helped, have a nice day!
-Aadi x
b) The cost (x) for hiring and artist for a stage show for (y) hours is represente
as 2y + x = 20.
Draw the graph 2y + x = 20 on the grid below.
[4]
The easiest way is to transform this equation to intercept form of straight line.
[tex]\\[/tex]
Intercept form of straight line:
[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex]where [tex]a[/tex] is the x intercept - where the graph intersects the x axis, and [tex]b[/tex] is the y intercept - where the graph intersects the y axis.
[tex]\\[/tex]
Given that,
[tex]2y + x = 20[/tex]
[tex] \longrightarrow \: \dfrac{2}{20}y + \dfrac{x}{20} = 1[/tex]
[tex] \longrightarrow \: \dfrac{x}{20} + \dfrac{y}{10} = 1[/tex]
On comparing with [tex]\dfrac{x}{a}+\dfrac{y}{b}=1,[/tex] we get,
[tex]a=20[/tex][tex]b=10[/tex]Hence, the graph shall cut the x axis and y axis at 20 and 10 respectively. This information is enough to plot the graph.
[tex]\\[/tex]
Graph: Refer to the attachment.
Lucy and Ayu sold a total of 1,080 iPads. Lucy sold 7 times as many as Ayu. How many did each sell
Answer:
let L=lucy and A=ayu
l+a=1080
l=7a 7a+a=1080
8a=1080 8a/8=1080/8
ayu=135
l=7a l=7×135
l=945 so:-135+945=1080
Lucy sold 945 iPads and Ayu sold 135 iPads
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
Let Lucy and Ayu sold 'x' and 'y' iPads respectively.
Lucy and Ayu sold a total of 1,080 iPads.
So, we get an equation,
⇒ x + y = 1080 ...............(i)
Lucy sold 7 times as many as Ayu.
So we get the second equation as,
⇒ x = 7y ................(ii)
Substitute above value of x in equation (i)
⇒ x + y = 1080
⇒ 7y + y = 1080
⇒ 8y = 1080
⇒ y = 135
This means, Ayu sold 135 iPads
Substitute above value of y in equation (ii)
⇒ x = 7(135)
⇒ x = 7 × 135
⇒ x = 945
This means, Lucy sold 945 iPads.
Therefore, Lucy sold 945 iPads and Ayu sold 135 iPads
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A petri dish is a small, shallow dish of thin glass or plastic, used especially for cultures in bacteriology. A 2-inch-radius petri dish, containing nutrients upon which bacteria can multiply, is smeared with a uniform suspension of bacteria. Subsequently, spots indicating colonies of bacteria appear. The distance of the center of the first spot to appear from the center of the petri dish is a variable with density curve y= x/2 for 0 < x <2 and y=0 otherwise.
a. Graph the density curve of this variable.
b. Show that the area under this density curve to the left of any number x between 0 and 2 equals x2/4.
c. What percentage of the time is the distance of the center of the first spot to appear from the center of the petri dish
1. at most 1 inch?
2. between 0.25 inch and 1.5 inches?
3. more than 0.75 inch?
Answer:
a) attached below
b) Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
C) i)25% ii) 54.69% iii) 85.94%
Step-by-step explanation:
Given density curve y = x/2 for 0 < x < 2 and y = 0
a) Graph the density curve of this variable
attached below
b) show that the area under the density curve to the left of any number x between 0 and 2 equals x^2/4
base of triangle = x
height = x/2
Hence to show the area under the density curve is equal to x^2/4 we will calculate the area to the left
Area = 1/2 ( base ) (height )
= 1/2 ( x ) ( x/2)
= x^2 / 4
c) Determine the percentage of the time of the distance of the center of the first spot to appear from the center of the petri dish
i) At most 1 inch
(area to the left of 1 ) = 1^2 / 4
= 1/4 = 0.25 ≈ 25%
ii) between 0.25 inch and 1.5 inches?
( area between 0.25 and 1.5 ) = ( area to the left of 1.5 ) - ( Area to the left of 0.25 )
= (1.5^2 / 4 )- ( 0.25^2 / 4 )
= 0.5469 = 54.69%
iii) more than 0.75 inch
( Area to the right of 0.75 ) = 1 - (0.75^ / 4)
= 0.8594 = 85.94 %
(11a2b+17a-4b2+15)+(12a2b-16b2+3)=
Answer:
232−202+17+18
Find the area of the polygon.
Answer:
240
Step-by-step explanation:
Hello There!
Note: the little arrows indicate that the line can be extended and it's opposite side will never touch indicating that it's a parallelogram
The formula for area of a parallelogram is
[tex]A=bh[/tex]
where b = base and h = height
the given dimension are
height = 15
base = 16
so all we have to do is plug in the values into the formula
[tex]A=(15)16\\15*16=240\\A=240[/tex]
so we can conclude that the area of the polygon is
240 square units
8. Misty created the number pattern below. 32, 28, 24, 20, ... If n represents a number in this pattern, which rule could be used to find the next number in the pattern?
Answer:
An = 32 - (4*(n-1))
Step-by-step explanation:
the starting term for this pattern is 32 (which you will need to include in the "rule")
you also know that the next term is the previous term - 4
so!
we can write this pattern as
An = 32 - (4*(n-1))
An = any number of term in the pattern
- ex). A2 = 28, A3 = 24, etc
n = the nth term
- the 3rd term = 24, the fourth term = 20, etc
Plz help me! Plz it’s due today,!
Answer: I think it is D
Step-by-step explanation:
in volume you multiply all the numbers(LxWxH)
hope this helps
What is the value of the expression below when x=7?
6x+ 10
A. 52
B. 67
C. 42
D.77
Answer:
52
Step-by-step explanation:
when a letter is next to a number like that and they tell u what the letter is u times it so 6x7+10=52 hope this helped :P
A taxi charges 2.50 plus .50 fee for each mile. If the ride costs 7.50 how many miles did he travel
Answer: 10 miles
Step-by-step explanation:
Mile 1: 3.00
Mile 2: 3.50
Mile 3: 4.00
Mile 4: 4.50
Mile 5: 5.00
Mile 6: 5.50
Mile 7: 6.00
Mile 8: 6.50
Mile 9: 7.00
Mile 10: 7.50
Please answer the questions below
Answer:
15 cm²
Step-by-step explanation:
The equation of the line that contains the points (-8, 1) and (0, -5) is
Answer:
y = -3/4x -5 (G)
Step-by-step explanation:
Find the slope by using the slope formula. (It's hard to format here so look it up)
Basically, it is y2 - y1/x2 - x1
-5 - 1/ 0 + 8
-6/8 = -3/4
The slope is -3/4.
Plug in for y = mx + b
y (y coordinate) = -5
x (x coordinate) = 0
slope (m) = -3/4
-5 = -3/4(0) + b
-5 = 0 + b
b = -5
y = -3/4x -5