Answer:
For 0,90 of Confidence we reject H₀
For 0,95 CI we reject H₀
Step-by-step explanation:
To evaluate a difference between two proportion with big sample sizes we proceed as follows
1.-Proportion 1
n = 2160
243 had rear license p₁ = 243/2160 p₁ = 0,1125
2.Proportion 2
n = 358
55 had rear license p₂ = 55/ 358 p₂ = 0,1536
Test Hypothesis
Null Hypothesis H₀ ⇒ p₂ = p₁
Alternative Hypothesis Hₐ ⇒ p₂ > p₁
With signficance level of 0,05 means z(c) = 1,64
T calculate z(s)
z(s) = ( p₂ - p₁ ) / √ p*q ( 1/n₁ + 1/n₂ )
p = ( x₁ + x₂ ) / n₁ + n₂
p = 243 + 55 / 2160 + 358
p = 0,1183 and then q = 1 - p q = 0,8817
z(s) = ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160 + 1 / 358)
z(s) = 0,0411 /√ 0,1043*0,003256
z(s) = 0,0411 / 0,01843
z(s) = 2,23
Then z(s) > z(c) 2,23 > 1,64
z(s) is in the rejection region we reject H₀
If we construct a CI for 0,95 α = 0,05 α/2 = 0,025
z (score ) is from z- table z = 1,96
CI = ( p ± z(0,025*SE)
CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )
CI = ( 0,1536 ± 1.96*0,01843)
CI = ( 0,1536 ± 0,03612 )
CI = ( 0,11748 ; 0,18972 )
In the new CI we don´t find 0 value so we have enough evidence to reject H₀
Which expression is equivalent to 6 cubed? 6 times 3 6 times 6 times 6 6 times 6 times 6 times 6 3 times 3 times 3 times 3 times 3 times 3
The expression that is equivalent to 6 cubed is: 6 times 6 times 6.
This is true since cubed indicates that the base number is multiplied by itself 3 times.
So, 6^3 equates to 6 x 6 x 6.
Answer:
The expression that is equivalent to 6 cubed is: 6 times 6 times 6.
This is true since cubed indicates that the base number is multiplied by itself 3 times.
So, 6^3 equates to 6 x 6 x 6.
Step-by-step explanation:
You are out with friends. Half of you want to go bowling and the other half want to go to a movie. How will you make a fair decision about wether to go to a movie or go bowling using a fair coin and assuming that all of you want to go to either of the places together?
Answer:
A fair coin because at the end of the day it will be fun no matter where you guys go
Step-by-step explanation:
0.25 multiplied by 15 = ?
What is ?
Answer:
Your correct answer is 3.75
Step-by-step explanation:
0.25 x 15 = 3.75
Answer:
3.75
Step-by-step explanation:
You can do this many ways. Write a table that looks like this:
0.25
15
--------
Ignore all decimal points. Multiply the 5's together and carry the 2 to the next column. Multiply 2 x 5 + 2, write the second digit (which is 2) and carry the 1. Multiply 0 by 5 + 1 = 1, so your top number should be 125. Then, multiply all the numbers by the 1. 5 x 1 = 5; 2 x 1 = 2; 0 x 1 = 0. We now have something that looks like:
0.25
15
--------
1 2 5
0 2 5
Add these numbers together and add the decimal point 2 numbers from the right, since that's what was in the original decimal.
1 2 5
0 2 5
---------------
3.75
Find the standard divisor to two decimal places (hundredth) for the given population and number of representative seats.
Population : 140,000
# seats : 9
A) 15,555.56
B) 17,055.56
C) 13,056
D) 14,055.56
E) 16,055
Answer:
A
Step-by-step explanation:
A divisor refers to a number by which another number is to be divided.
So what this question is practically asking us is that which of the values in the options to 2 decimal places is the result dividing the population by the number of seats
Thus we have;
140,000/9 = 15,555.55555 which to 2 decimal places is 15,555.56
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y=x^{3 / 2}, \ y=8, \ x=0y=x 3/2, y=8, x=0
Answer:
The volume of the solid using shell method is V= π(284/7)
Step by step Explanation:
Shell method is a method device to calculate the volume of a solid of revolution.
From the question, we were given
y=x³/₂
y=8,
x=0
then f(x)=8-x³/₂
The volume we were told to find , using the shell formula can be calculated using below formula
V=2π∫xf(x)dx
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
17. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. How large a sample is need it if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean
Answer:
A sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.
Step-by-step explanation:
We are given that an electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours.
We have to find a sample such that we are 98% confident that our sample mean will be within 4 hours of the true mean.
As we know that the Margin of error formula is given by;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\sigma[/tex] = standard deviation = 40 hours
n = sample size
[tex]\alpha[/tex] = level of significance = 1 - 0.98 = 0.02 or 2%
Now, the critical value of z at ([tex]\frac{0.02}{2}[/tex] = 1%) level of significance n the z table is given as 2.3263.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
[tex]4=2.3263 \times \frac{40}{\sqrt{n} }[/tex]
[tex]\sqrt{n}= \frac{40 \times 2.3263}{ 4}[/tex]
[tex]\sqrt{n}=23.26[/tex]
n = [tex]23.26^{2}[/tex] = 541.03 ≈ 541
Hence, a sample of at least 541 is needed if we wish to be 98% confident that our sample mean will be within 4 hours of the true mean.
which is true about the solution to the system of inequalities shown?
A) y ≥ 1/3x + 3 AND 3x - y > 2
B) y ≥ 1/2x + 3 AND 3x - y > 2
C) y ≥ 1/3x + 3 AND 3x + y > 2
D) y ≥ 1/3x + 3 AND 2x - y > 2
Answer:
the solution to the system of inequality is C
Find the volume of each solid. Round to the nearest tenth. IMG_7097.HEIC
Answer:
You didn't put an attachment to show what solid you wanted rounded
Step-by-step explanation:
How many ten-digit numbers have at least two equal digits?
Please explain!
Between 1,000,000,000 and 9,999,999,999 there are 9,000,000,000 different ten-digit numbers. Of those, 9*9! (9 times 9 factorial) = 3,265,920 have all ten digits different, i.e., no two equal digits. Take the difference of those two numbers, and you will have your answer.
--------------------
Hope this helps!
Brainliest would be great!
--------------------
With all care,
07x12!
Subtracting polynomials
Answer:
-11xy
Step-by-step explanation:
Subtracting a negative means adding.
-14xy - (-3xy) = -14xy + 3xy = -11xy
Dertemine the direction that this parábola opens: y=-x^2-2x-5 (up or down)
Answer:
down
Step-by-step explanation:
x is negative
A loan of $25,475 is taken out at 4.6% interest, compounded annually. If no payments are
made, after about how many years will the amount due reach $37,500? Round to the
nearest year.
Please helpp
Answer:
9 years
Step-by-step explanation:
I have attached the file
Answer:
sorry i am not able to understood
Step-by-step explanation:
which basic geometric figure is labeled as cd
Answer:
a geometric figure labeled CD would be a segment
Step-by-step explanation: you need to attached the pictures with the question
Yo tenía $5
Mi mamá me dió $10
Mi papá me dió $30
Mi tío y mi tía me dieron $100
Yo tenía otros $20
¿Cuánto tenía?
Answer:
$25
Step-by-step explanation:
De la pregunta anterior, se nos da la siguiente información
Yo TENÍA $ 5
Mi mamá me dió $ 10
Mi papá me dió $ 30
Mi tío y mi tía me dieron $ 100
Yo TENÍA otros $ 20
Si miras arriba, notarás que la palabra TENÍA está en mayúscula.
Esto se debe a que para resolver esta pregunta correctamente, tenemos que concentrarnos o prestar atención a los tiempos verbales del inglés que se usan al hacer la pregunta.
La pregunta dice: ¿Cuánto tenía?
Esto significa que la pregunta anterior es sobre cuánto tenía en el pasado antes de que sus padres, tío y tía le dieran dinero.
Por lo tanto, la cantidad de dinero que tenía
= $20 + $5
= $ 25
The total amount I have altogether will be $165
In order to get the total amount that you have, we will add all the cash you were given and the ones you have altogether.
Amount initially owned = $5
Amount given by relatives = $10 + $30 + $100
Amount given by relatives = $140
If he has another $20
Total amount I have = $5 +$140 + $20
Hence the total amount I have altogether will be $165
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Sam borrows $5700 at 4.5% simple interest for 3 years. Find the interest
Answer:
The interest is
$ 769.50Step-by-step explanation:
Simple interest is given by
[tex]I = \frac{P \times R \times T}{100} [/tex]
where
P is the principal
R is the rate
T is the time given
From the question
The principal / P = $ 5700
The rate / R = 4.5%
The time given / T = 3 years
So the interest is
[tex]I = \frac{5700 \times 4.5 \times 3}{100} [/tex]
[tex]I = \frac{76950}{100} [/tex]
We have the final answer as
I = $ 769.50
Hope this helps you
In the diagram below, AB is parallel to CD. What is the value of X?
A. 60
В. 100
C.120
D. 80
The vector x is in a subspace H with a basis Bequals{Bold b 1,Bold b 2}. Find the B-coordinate vector of x. Bold b 1equals[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 3 EndMatrix ], Bold b 2equals[Start 3 By 1 Matrix 1st Row 1st Column negative 4 2nd Row 1st Column negative 7 3rd Row 1st Column 11 EndMatrix ], xequals[Start 3 By 1 Matrix 1st Row 1st Column negative 10 2nd Row 1st Column negative 17 3rd Row 1st Column 27 EndMatrix ]
Answer and Step-by-step explanation: To find the B-coordinate vector of x:
[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]
The augmented matrix will be:
[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]
Transforming into reduced row-echelon form:
= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]
The values for the vector will be:
x = 2
y = 3
The B-coordinate vector is of the form:
V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]
The General Social Survey (GSS) is a sociological survey used to collect data on demographic characteristics and attitudes of residents of the United States. In 2010, the survey collected responses from over a thousand US residents. The survey is conducted face-to-face with an in-person interview of a randomly-selected sample of adults. One of the questions on the survey is "For how many days during the past 30 days was your mental health, which includes stress, depression, and problems with emotions, not good?" Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24 days in 2010. Given this information, which of the following statements would be most appropriate to make regarding the true average number of days of "not good" mental health in 2010 for US residents? 1 point For these 1,151 residents in 2010, we are 95% confident that the average number of days of "not good" mental health is between 3.40 and 4.24 days. There is not sufficient information to calculate the margin of error of this confidence interval. For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days.
The most appropriate statement is the one that correctly reflects the confidence interval obtained from the survey data, as stated above.
The most appropriate statement to make regarding the true average number of days of "not good" mental health in 2010 for US residents, based on the given information, is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
The 95% confidence interval of 3.40 to 4.24 days is obtained from the survey data, and it provides an estimate of the range within which the true average number of days of "not good" mental health falls for the entire population of US residents.
Regarding the provided options:
There is not sufficient information to calculate the margin of error of this confidence interval: This statement is not accurate since the margin of error can be calculated using the formula Margin of Error = (Upper Limit - Lower Limit) / 2.
For all US residents in 2010, based on this 95% confidence interval, we would reject a null hypothesis stating that the true average number of days of "not good" mental health is 5 days: This statement is not supported by the given information. The confidence interval provides an estimate of the range within which the true average lies, but it does not involve a comparison to a specific value such as 5 days.
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Based on the provided information and the 95% confidence interval of 3.40 to 4.24 days for "not good" mental health in 2010,
The most appropriate statement to make regarding the true average number of days of "not good" mental health for US residents in 2010 is:
"For these 1,151 residents in 2010, we are 95% confident that the average number of days of 'not good' mental health is between 3.40 and 4.24 days."
This statement accurately represents the confidence interval obtained from the survey data.
It indicates that the true average number of "not good" mental health days for the entire US population in 2010 is likely to fall within this range with a 95% level of confidence.
It's important to note that this statement only applies to the specific sample of 1,151 US residents surveyed in 2010.
To make inferences about the true average number of "not good" mental health days for all US residents in 2010, a different sample with a larger representative size would be required.
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3) The average age of students at XYZ University is 24 years with a standard deviation of 8 years. Number of students at the university is 7500. A random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years
Answer:
0.1875
Step-by-step explanation:
σM=σ/√N
=8/√7500
=8/86.608
=0.092
Z=(x-μ)/σ/√N
=(25.5-36)/8/√7500
=-10.5/0.0092=-1141.304
Z score = -1.3125
=(27-36)/8/√7500 =
=9/0.0092=978.261
Z score= -1.125
-1.125-(-1.3125)=-1.125+1.3125)= 0.1875
The probability that the sample mean will be between 25.5 and 27 years
P(between 25.5 and 27) = 0.1875
Find the slope of the line passing through the points (-3, -8) and (4,6).
Answer:
slope = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have
[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]
Substitute:
[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]
The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:
[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]
We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:
[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]
[tex]=\dfrac{14}{7}=2[/tex]
The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!
a store specializing in mountain bikes is to open in one of two malls if the first mall is selected the store anticipates a yearly profit of $825,000 if successful a yearly loss of 275,000 otherwise the probability of success is 1/2 if the second mall is selected it is an estimated that the yearly profit will be 550,000 if successful otherwise the annual loss will be 165,000 the probability of success at the second mall is three Force
Complete question :
a store specializing in mountain bikes is to open in one of two malls if the first mall is selected the store anticipates a yearly profit of $825,000 if successful a yearly loss of 275,000 otherwise the probability of success is 1/2 if the second mall is selected it is an estimated that the yearly profit will be 550,000 if successful otherwise the annual loss will be 165,000 the probability of success at the second mall is three Fourth (3/4).
What is the expected profit of thesecond mall?
Answer:
$453,750
Step-by-step explanation:
Given the following :
First mall:
Profit if successful = $825,000
Loss if otherwise = $275000
Probability of success = 1/2
Second mall:
Profit if successful = $550,000
Loss if otherwise = $165,000
Probability of success = 3/4
Expected profit of second mall:
If probability of profit ' P(profit)' = 3/4
Then,
Probability of loss P(loss) = 1 - P(profit)
P(loss) = 1 - 3/4 = 1/4
Expected profit:
[P(profit) * profit] + [P(loss) * loss])
(0.75 * $550,000) + (0.25 * (-$165,000))
$412,500 - $41,250 = $453,750
how many solutions if both slopes are the same but the y-intercepts are different
Answer:
No solutions.
Step-by-step explanation:
You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.
Hope this helps!
Answer: no solution
Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.
Let's look at an example.
Below, you will see two equations.
Both of the lines have a slope of 1.
So, they must be parallel which means they don't cross.
So there is no solution.
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 249 cubic units.
What is the height of the cylinder?
O2 units
4 units
O 6 units
O 8 units
Answer:
h = 6 unitsStep-by-step explanation:
Volume of a cylinder = πr²h
where r is the radius
h is the height
The height of a right cylinder is 3 times the radius of the base is written as
h = 3r
Volume = 249cubic units
So we have
249 = π r²(3r)
249 = π3r³
Divide both sides by 3π
r³ = 249/3π
r = 2
h = 3(2)
h = 6 units
Hope this helps you
A college dining hall took a survey of 260 students on their favorite meals. one fifth of students selected macaroni and cheese as their favorite and 15% selected breakfast as their favorite answer. How many students chose a food other than the two above?
a. 52
b. 65
c. 91
d.169
Answer:
d. 169
Step-by-step explanation:
1/5 * ( 260) = 52
0.15 ( 260)= 39
out of 260 students 39 + 52 = 91 students chose a food / meal
the rest are 260 - 91 = 169 students chose a food other than the two
a number is one more than twice the other number. their product is 36. what are the numbers
Answer:
Possible solution 1: -4.5 and -8
Solution 2: 4 and 9.
Step-by-step explanation:
Let the two numbers be a and b.
One of them (let it be b) is 1 more than twice the other one. In other words,
b= 1+ 2a.
Their product is 36. Or:
a(b) = 36.
Substitute b:
a(1+2a) = 36
2a^2 + a = 36
2a^2 + a - 36 = 0
This is now a quadratic. We can factor to solve it. Find two numbers that equals 2(-36)=-72 and add to 1. We can use 9 and -8. Thus:
2a^2 - 8a + 9a - 36 = 0
2a(a - 4) +9(a-4) = (2a+9)(a-4) = 0
So, a = -9/2 = -4.5 or a = 4.
Thus, b can equal 1 + 2(-4.5) = -8 or 1 + 2(4) = 9
g The equation for the change of position of a train starting at x = 0 m is given by The dimensions of b are Select one: a. L-1T-1 b. LT-1 c. T-3 d. LT-2 e. LT-3
Answer:
B. LT⁻¹Step-by-step explanation:
The question is incomplete. Here is the complete question,
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .
Since velocity is the rate of change of displacement of a body, then;
VELOCITY = DISPLACEMENT/TIME
displacement is measured in metres while time in seconds.
expressing the formula in terms of its fundamental unit,
v = metre/secs
Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;
V = L/T
V = L * 1/T
V = L * T⁻¹
V = LT⁻¹
Hence the dimension of b is LT⁻¹.
Note that the dimension of a body is written in terms of its fundamental quantities.
The dimensions of b from the given equation are; B: LT⁻¹
Dimensional Analysis
The complete question is;
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹
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Determine the relationship between the measure of angle ADE and the measure of arc AE by circling one of the statements below.
Answer:
The answer c is correct.
Step-by-step explanation:
When two chords share an endpoint, the inscribed angle has half of the measure of the intercepted arc. In this example, ADE is the inscribed angle, so its measure is one half of the arc AE's measure. m<ADE= 1/2(mAE)
i hope this helped :)
The relationship between the measure of angle ADE and the measure of arc AE is m∠ADE = [tex]\frac{1}{2}[/tex] m (arc AE) .
What seems to be the relationship between an inscribed angle and its intercepted arc?The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent. This is called the Congruent Inscribed Angles Theorem
According to the question
The relationship between the measure of angle ADE and the measure of arc AE .
∠ADE is a inscribed angle
arc AE is a intercepted arc
According to Inscribed Angle Theorem
∠ADE = [tex]\frac{1}{2}[/tex] arc AE
Hence, the relationship between the measure of angle ADE and the measure of arc AE is m∠ADE = [tex]\frac{1}{2}[/tex] m (arc AE) .
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Answer the following question by entering the numeric value with appropriate units. If the length of one side of a square is 12.0 mm, what is the perimeter of the square? Express the perimeter with the appropriate units.
Answer:
48.0 mm
Step-by-step explanation:
A square has 4 equal sides. If one side is 12.0 mm the ll 4 sides are the same. so you can just multiply 12*4 and get 48.0 mm. That would be the answer. The second way to solve it is to add 12 .0 mm 4 times and you would get 48.0 mm.
A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation A pizza delivery company buys 54 of these cars. What is the probability that the average mileage of the fleet is between 33.3 and 34.3 mpg?
Answer:
[tex] z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028[/tex]
[tex] z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441[/tex]
An we can use the normal standard table and the following difference and we got this result:
[tex] P(-1.028<z<0.441)= P(z<0.441) -P(z<-1.028) = 0.670 -0.152 =0.518[/tex]
Step-by-step explanation:
Assuming this statement to complete the problem "with a standard deviation 5 mpg"
We have the following info given:
[tex]\mu = 34[/tex] represent the mean
[tex]\sigma= 5[/tex] represent the deviation
We have a sample size of n = 54 and we want to find this probability:
[tex] P(33.3 < \bar X< 34.3)[/tex]
And for this case since the sample size is large enough >30 we can apply the central limit theorem and then we can use this distribution:
[tex]\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028[/tex]
[tex] z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441[/tex]
An we can use the normal standard table and the following difference and we got this result:
[tex] P(-1.028<z<0.441)= P(z<0.441) -P(z<-1.028) = 0.670 -0.152 =0.518[/tex]