Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
In a class of 12 boys and 8 girls, two students need to be chosen for classroom jobs.
What is the probability that Mary gets selected?
Answer:
55 percent chance or 11/20 or 0.55
Step-by-step explanation
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
A. (195 - 286) + 1.992 underroot46/45 + 58/40
B. (286 - 195) + 1.992 underroot46^2/45+ 58^2/40
C. (195 - 286)+ 1.992 underrot 140² 158²/45+40
D. (286 - 195) + 1.992 46 1582 45 +40
E. (195-286) +1.992 462 + 58 45 40
Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
Learn more about confidence interval here:
https://brainly.com/question/4249560
Lourdes recorded in this table the change in her dog's weight, in ounces, each month. Which statement can be suppor by the data in the table? Change in Dog's Weight January February March April May +6 +4 -2 +1 -5
A) Lourdes dog gained weight in more months than it lost weight because there are more positive numbers than ne numbers.
B) Lourdes' dog lost weight in more months that it gained weight because the digit 5 is the greatest digit and it is a ne number.
C) Lourdes dog gained weight every month because it is getting older.
D) Lourdes dog lost weight every month because the change in May is a negative number.
Answer:
A). Lourdes dog gained weight in more months than it lost weight because there are more positive numbers then negative numbers
8. Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC
Step-by-step explanation:
Angle ADB = Angle CBD = 90° (given)
Side AB = Side DC (given)
Common side DB / BD
By HL congruence, triangles ABD and CDB are congruent.
Therefore Angle ABD = Angle CDB
=> Line AB is parallel to Line DC (Z angles)
Where did the 45% come from. It states 55% in question
Answer:
is this a question......
A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?
A. $ 58.50
B. $ 80
C. No, it did not mark up 30%.
Step-by-step explanation:Since,
A. We have,
Mark up percentage = 30%
Actual price = $ 45,
B. We have,
SP = $ 104,
C. We have,
AP = $ 75,
SP = $100,
Thus, mark up percentage =
= 33.33 %
Hence, store did not mark up the price by 30%.
What is the answer I need help pls
Answer:
The answers are,
-3, -7
-2, 4
0, 2
2, 8
3, 11
Step-by-step explanation:
You just plug in the domain values into the equation and solve for f(x), so your domain number is your x value and the y value(f(x) value) is the answer
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
Answer: It is a function because at any given time the oven was exactly one temperature.
Step-by-step explanation:
It is given that:
At 5:00 p.m., Antonio turned on the oven.
The oven remained at 400°F for 45 minutes until Antonio turned it off.
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m.
Find the value of x. Everything is in the photo.
Answer:
27
Step-by-step explanation:
Note that since VX and XZ are both line segments, <VWX and <XYZ both equal 180 (also known as a straight angle). Also, note that the sum of the angles in a triangle are 180 degrees. Now, let’s start.
Finding angles of the triangle:
<WYX = <XYZ - <WYZ = 180 - 4x
<XWY = <XWV - <VWY = 180 - 6x
Using the sum of angles in a triangle and substituting these values in:
180 = <X + <WYX + <XWY = 90 + (180 - 4x) + (180-6x) = 450 - 10x
270 = 10x
27 = x
We are done! I hope this helps! :)
16 is what percent of 20?
Answer:
3.2
Step-by-step explanation:
Which of the following is not a solution of the equation y=3x-4?
A. 2,2
B. 0,-4
C. 4,8
D. -1,-1
Nick earns 3.5%
commission on every
car he sells. How much
would he earn if he sold
a $14.000 car?
The amount he would earn is $490.
What does multiplication mean?
Multiplication is the process of determining the product of a number. It is determined by following some mathematical processes. The sign used to represent multiplication is ×.
How much will he earn?Commission = 3.5% x $14,000
0.035 x $14,000 = $490
To learn more about multiplication, please check: https://brainly.com/question/13814687
-3(1)+(-3)(-1) =
+()]
-3(1) + (-3)(-1)=-3[0]
-3(1)+(-3)(-1) =
_
+(-3)(-1) =
+
Answer:
³⅜
Step-by-step explanation:
⁴⁵⅖
+⁷⅝×⅖i
I HOPE IT HELP TYSM
Answer:
i dunno
Step-by-step explanation:
Pls help me with this ASAP
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?
Answer
a. 0.856
b. 0.78071
c. It is not unusual
d. 13.65 years old
Step-by-step explanation:
The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.
We solve this question using z score formula:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Find the probability that a cat will live to be older than 14 years.
For x > 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x<14) = 0.144
P(x>14) = 1 - P(x<14) = 0.856
b. Find the probability that a cat will live between 14 and 18 years.
For x = 14 years
z = 14 - 15.7/1.6
z = -1.0625
Probability value from Z-Table:
P(x = 14) = 0.144
For x = 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x = 18) = 0.92471
The probability that a cat will live between 14 and 18 years is calculated as:
P(x = 18) - P(x = 14)
0.92471 - 0.144
= 0.78071
c. If a cat lives to be over 18 years, would that be unusual? Why or why not?
For x > 18 years
z = 18 - 15.7/1.6
z= 1.4375
Probability value from Z-Table:
P(x<18) = 0.92471
P(x>18) = 1 - P(x<18) = 0.075288
Converting this to percentage:
0.075288 × 100 = 7.5288%
Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.
d. How old would a cat have to be to be older than 90% of other cats?
From the question above, 10% of the cats would be older than 90% of other cats.
Hence, we find the z score of the 10th percentile
= -1.282
Hence,
-1.282 = x - 15.7/1.6
Cross Multiply
-1.282 × 1.6 = x - 15.7
- 2.0512 = x - 15.7
x = 15.7 -2.0512
x = 13.6488 years old
Approximately = 13.65 years old
Which substitution method should be the best used to solve which system of equations
Answer: 6x+2y=1
Step-by-step explanation:
because it just is