Answer:
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
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 normally distributed samples are 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.
In this question, we have that:
[tex]\mu = 74000, \sigma = 2500, n = 36, s = \frac{2500}{\sqrt{36}} = 416.67[/tex]
What is the probability that the mean annual salary of the sample is between $71000 and $73500?
This is the pvalue of Z when X = 73500 subtracted by the pvalue of Z when X = 71000. So
X = 73500
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{73500 - 74000}{416.67}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151
X = 71000
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{71000 - 74000}{416.67}[/tex]
[tex]Z = -7.2[/tex]
[tex]Z = -7.2[/tex] has a pvalue of 0.
0.1151 - 0 = 0.1151
11.51% probability that the mean annual salary of the sample is between $71000 and $73500
While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.
Find your monthly expense.
Hey there! I'm happy to help!
Let's add up all of these contributions.
100+300+150+450=1000
However, this is annual. We want monthly. So, we simply divide by 12.
1000/12≈83.33
Therefore, the monthly expense is $83.33
I hope that this helps! Have a wonderful day!
When writing expressions for complex numbers, what does i represent?
Answer: See below
Step-by-step explanation:
[tex]i[/tex] is an imaginary number.
[tex]i=\sqrt{-1}[/tex]
[tex]i^2=-1[/tex]
Nadeen is at an arcade. She started with 18 tokens. Each game costs 3 tokens. So far, Nadeen has played 2
games.
Answer:
see below
Step-by-step explanation:
I think you are asking how many tokens she has left. She has 18 - 3 * 2 = 18 - 6 = 12 tokens left. She can play 12/3 = 4 more games.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Step-by-step explanation:
The formula is y = mx + b
m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.
To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.
(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].
We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:
[tex]y=\frac{3}{4} x-4[/tex]
An on-line retailer identified the web browser being used by a sample of 50 shoppers to its online site. The accompanying data table identifies the browser being used by a shopper. Previously in 2010, 64% of shoppers used Browser A, 24% Browser B, 6% Browser C, 3% Browser D, and 3% Browser E.
Required:
a. Using software, tabulate the frequency of the choice of browser used by these shoppers.
b. Present a bar chart and a pie chart of these frequencies. Which is more useful to compare the distribution of these to those observed in 2010?
c. Do you see any changes in the distribution of the choice of browser?
Answer:
See Explanation
This question is answered using Microsoft Office Excel 2013
Step-by-step explanation:
Given
Browser A - 64%
Browser B - 24%
Browser C - 6%
Browser D - 3%
Browser E - 3%
Total Frequency = 50
a.
To tabulate the frequency of the choice of browser, the total frequency is multiplied by each individual percentage as follows;
Browser A - 64% * 50 = 32
Browser B - 24% * 50 = 12
Browser C - 6% * 50 = 3
Browser D - 3%* 50 = 1.5
Browser E - 3% * 50 = 1.5
See Attachment for frequency table (using software)
b. See Attachment for pie chart and bar chart.
Both charts are useful for data presentation but in this case, the pie chart is a better option to use because it shows how the distribution of each browser and how they make up as a whole.
The main circle of the pie chart shows how individual browser are distributed through segments; This is not so for the bars of the bar chart which.
c. Yes, there are changes in the choice of browser.
Aside from Browser D and E that has the same frequency, other browsers (A-C) have different frequency.
Also, the distribution shows that more users make use of browser A than other browsers and the least frequent used browser are browser D and E.
What is the indicated missing angle can someone pls help me
Answer:
30
Step-by-step explanation:
Since this is a right triangle, we can use a trig function
cos theta = adjacent/ hypotenuse
cos ? = 52/ 60
Take the inverse cos of each side
cos ^ -1 cos ? = cos ^ -1 ( 52/60)
? =29.92643487
To the nearest degree
? = 30
[tex]answer \\ 30 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
How did governments pursue mercantilist policies?
Answer:
Most of the mercantilist policies were the outgrowth of the relationship between the governments of the nation-states and their mercantile classes
Step-by-step explanation:
In the British empire Mercantilism, an economic policy designed to increase a nation's wealth through ... Mercantilism did, however, lead to the adoption of enormous trade
Hope this helps. :)
Which expression is equivalent to 3(x-6)+5(x-4)
Answer:
[tex]8x-38[/tex]
Step-by-step explanation:
[tex]3(x-6)+5(x-4)\\3x-18+5x-20\\3x+5x-18-20\\8x-38[/tex]
I need help with solving this
Answer:
49
Step-by-step explanation:
Positive 49 not -49
What is the quotient 5^-6 over 5^3
Answer:
1/ 5^9
Step-by-step explanation:
5^-6/5^3
5^(-6-3)
5^-9
Final Answer - 1/5^9
x^2 + 5x - 24 = 0 How do I solve by factoring
Answer:
x = -8 or x = 3
Step-by-step explanation:
To factor ax² + bx + c, use AC method.
a times c is 1 × -24 = -24.
Factors of ac (-24) that add up to b (5) are 8 and -3.
Divide by a and reduce: 8/1 and -3/1.
Therefore, the factors are x + 8 and x − 3.
x² + 5x − 24 = 0
(x + 8) (x − 3) = 0
x = -8 or 3
A U.S.-based Internet company offers an online proficiency course in basic accounting. Completing this online course satisfies the "Fundamentals of Accounting" course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. Region Enrollment 1 45 2 60 3 30 4 40 5 50 6 55 7 35 The CEO looked at the data presented and said no they are not equal. It is obvious, since the enrollment in one region is 60 and another 30. However, the CFO said that using a Chi-Square Goodness of Fit Test with a 1% significance level, the frequencies in the regions are not significantly different. Which one is correct? Use statistics to support your answer.
Answer:
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
The Chi - Square Value = 15.556
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
Step-by-step explanation:
From the question; Let state our null hypothesis and alternative hypothesis
Null Hypothesis
[tex]\mathbf{H_0:}[/tex]There is equal number of average interest in the course across all regions.
Alternative Hypothesis
[tex]\mathbf{H_a:}[/tex] At least one of the region differs in average number of interest in the course.
The table can be better structured as :
Region Enrollment
1 45
2 60
3 30
4 40
5 50
6 55
7 35
From above; we know the number of sample = 7
Then our expected mean can be calculated as :
[tex]Expected \ mean = \dfrac{sum \ of \ values }{n}[/tex]
[tex]Expected \ mean = \dfrac{315 }{7}[/tex]
Expected mean = 45
SO, let's construct our Chi-Square Statistics Test Table as follows:
Observed Expected Expected (O-E)² [tex]\dfrac{(O-E)^2}{E}[/tex]
(O) (E) proportion
45 45 0.142857 0 0
60 45 0.142857 225 5
30 45 0.142857 225 5
40 45 0.142857 25 0.556
50 45 0.142857 25 0.556
55 45 0.142857 100 2.222
35 45 0.142857 100 2.222
15.556
The Chi - Square Value = 15.556
Degree of freedom = n- 1
Degree of freedom = 7 - 1
Degree of freedom = 6
Level of significance ∝ = 1% = 0.01
The Critical value of Chi Square test statistic at df = 6 and 0.01 significance level is 16.812
The Decision rule is to reject the Null hypothesis if The Chi Square test statistic X² > 16.812
Thus , since the Chi Square test statistic is lesser than the critical value,
i.e 15.556 < 16.812 ,we accept null hypothesis [tex]\mathbf{H_0}[/tex]
Conclusion:
We conclude that there is equal number of average interest in the course across all regions.
Thus, the CFO is correct, the the frequencies in the regions are not significantly different by using a Chi-Square Goodness of Fit Test with a 1% significance level.
What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …
Answer:
Next two numbers are 15 and 32 respectively.
Step-by-step explanation:
The given pattern is
45, 15, 44, 17, 40, 20, 31, 25, …
Here, we have two patterns.
Odd places : 45, 44, 40, 31,...
Even places : 15, 17, 20, 25,...
In series of odd places, we need to subtract square of integers.
[tex]45-(1)^2=45-1=44[/tex]
[tex]44-(2)^2=44-4=40[/tex]
[tex]40-(3)^2=40-9=31[/tex]
So, 9th term of given pattern is
[tex]31-(4)^2=31-16=15[/tex]
In series of even places, we need to add prime numbers.
[tex]15-2=17[/tex]
[tex]17+3=20[/tex]
[tex]20+5=25[/tex]
So, 10th term of given pattern is
[tex]25+7=32[/tex]
Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.
What is the perimeter of the shape below?
Answer:
I think it is 288.6 ft. Lol hope this helps
Step-by-step explanation:
write this small number in standard form. 0.00078
Answer:
78/100000
Hope it helps you
Which of the following statements is the converse of the statement, "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"? 1.) If two angles have equal measures, then the measure of each is 28 degrees. 2.) If two angles do not have equal measures, then each of the two angles does not have a measure of 28 degrees. 3.) If each of two angles does not have a measure of 28 degrees, then the two angles do not have equal measures. 4.) If each of two angles does not have a measure of 28 degrees, then the two angles have equal measures.
Answer:
1.) If two angles have equal measures, then the measure of each is 28 degrees.
Step-by-step explanation:
The converse of a statement simply swaps the positions of the "if" and "then" clauses. Without any modification for clarity or readability, the converse would be ...
if two angles are equal in measure, then each of the two angles has a measure of 28 degrees.
last year we had 250 of employees and due to attrion we lost 12% we only have blank employees left ?
Answer:
220
Step-by-step explanation:
If we lost 12% we still have 100 - 12 = 88% of the employees left. 88% can be written as 0.88. 0.88 * 250 = 220 employees left.
evaluate...
(2/1) to the power -2
Answer:
hope this helps :)
Step-by-step explanation:
1/4 because 2/1 is 2 and 2 to the power of -2 is 1/4
Find the value of x from this adjoining figure
Answer:
[tex]x=15^\circ[/tex]
Step-by-step explanation:
Please refer to the attached figure for labeling of given diagram:
We are given the following angles:
[tex]\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ[/tex]
Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.
Using property of vertically opposite angles:
[tex]\angle EOF = \angle AOB = 7x^\circ[/tex]
Line CD is a straight line, so [tex]\angle COD = 180^\circ[/tex]
Also,
[tex]\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ[/tex]
Hence, answer is [tex]x = 15^\circ[/tex].
At 2pm on Tuesday the temperature was -12
degrees. By 6pm the temperature dropped
to -20 degrees. What was the average
change in temperature each hour?
Answer:
-2×h
Step-by-step explanation:
because it drops-2 by hour so multiply-2 by the difference of hours
The following are daily outputs from shift A and shift B at a factory.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
Answer:
shift B
Step-by-step explanation:
shift a is 78.6 repeating
shift b is 79.3 repeating
mean is when you add them all then divide it by the numbers it has
Answer:
shift B
Step-by-step explanation:
To calculate the mean for a set of data, add all the numbers in that set, then divide by the number of data points in the set.
(12 /`15) ÷ (25/ 16) =
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
[tex]\frac{12}{15} \div \frac{25}{16}[/tex]
[tex]\frac{12}{15} \times \frac{16}{25}[/tex]
[tex]\frac{12 \times 16}{15 \times 25}[/tex]
[tex]\frac{192}{375}[/tex]
[tex]\frac{64}{125}=0.512[/tex]
Answer:
[tex]\frac{64}{125}[/tex]
Step-by-step explanation:
=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]
Changing the division sign into multiplication and inverting the term after the sign.
=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]
=> [tex]\frac{12*16}{15*25}[/tex]
=> [tex]\frac{192}{375}[/tex]
=> [tex]\frac{64}{125}[/tex]
This is the required form.
Find the sample space for picking a number from 1 to 3 and choosing red or white
Answer:
The event of picking a number from 1 to 3 consists of:
Pick number 1
Pick number 2
Pick number 3
The event of choosing red or white card consists of:
Choose a red card
Choose a white card
=> The sample space for picking a number from 1 to 3 and choosing red or white card:
Pick number 1 and choose a red card
Pick number 1 and choose a white card
Pick number 2 and choose a red card
Pick number 2 and choose a white card
Pick number 3 and choose a red card
Pick number 3 and choose a white card
Hope this helps!
:)
NEED GEOMETRY HELP ASAP
Answer:
HJ > KP
Step-by-step explanation:
Form the figure attached,
Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ
m∠HGJ = 90°
m∠KLP = 85°
Since m∠HGJ > m∠PLK
Therefore, measure of opposite sides of these angles have the same relation.
HJ > KP
Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76
Answer:
The critical values of F at 95% confidence are 0.359 and 2.788.
Step-by-step explanation:
We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:
Store A Store B
nA = 21 nB = 16
SA = 28.284 SB = 20
And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.
AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.
The test statistics for F-test is = [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex] ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]
where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.
Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;
2.788 for right-part and 0.359 for the left-part.
Which of the following numbers are in setA? Check all that apply.
A = {x | x is a positive, odd integer less than 7}
0
1
2
5
3
Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer: A
Step-by-step explanation:
To multiply matrices, multiply each term in Row 1 of the first matrix with each term in Column 1 of the second matrix and then find their sum. Repeat for Row1×Column2, Row2×Column1, and Row2×Column2.
[tex]\left[\begin{array}{ccc}1&4&-1\\3&2&2\end{array}\right] \times \left[\begin{array}{cc}2&-1\\0&3\\5&2\end{array}\right] \\\\\\=\left[\begin{array}{ccc}1(2)+4(0)-1(5)&1(-1)+4(3)-1(2)\\3(2)+2(0)+2(5)&3(-1)+2(3)+2(2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-3&9\\16&7\end{array}\right][/tex]
calculate the
Simple interest on a
7,500,00 for 4 years
at 4½
per
annum
Step-by-step explanation:
S.i =principal x rate x time/100
7,50000x4x4.5/100
13500000/100
135000
Let $A_1 A_2 A_3 A_4$ be a regular tetrahedron. Let $P_1$ be the center of face $A_2 A_3 A_4,$ and define vertices $P_2,$ $P_3,$ and $P_4$ the same way. Find the ratio of the volume of tetrahedron $A_1 A_2 A_3 A_4$ to the volume of tetrahedron $P_1 P_2 P_3 P_4.$
Answer:
27 : 1
Step-by-step explanation:
The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.
Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...
3³ : 1³ = 27 : 1
Choose the equation for the graph
below.
a. y =
1
X-2
2
b.y =
x²–4
3
c. y =
x+2
-3
d.y=
e. y =
2x+4
1
x2+2x+1
Answer:
C
Step-by-step explanation:
Plugged into calculator
Vertical asymptotes: x=-2
Horizontal asymptotes: y=0
No oblique asymptotes
