Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal.
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?
(b) What is the probability that the mean return will be less than 8%?
Answer:
a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.
b) 0.4129 = 41.29% probability that the mean return will be less than 8%
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 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 z-score 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 p-value, 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.
Mean 8.7% and standard deviation 20.2%.
This means that [tex]\mu = 8.7, \sigma = 20.2[/tex]
40 years:
This means that [tex]n = 40, s = \frac{20.2}{\sqrt{40}}[/tex]
(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?
This is 1 subtracted by the pvalue of Z when X = 13. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0885
0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.
(b) What is the probability that the mean return will be less than 8%?
This is the pvalue of Z when X = 8. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}[/tex]
[tex]Z = -0.22[/tex]
[tex]Z = -0.22[/tex] has a pvalue of 0.4129
0.4129 = 41.29% probability that the mean return will be less than 8%
Given that MTW = CAD, which segments are corresponding parts of the congruent triangles?
Answer: MW = CD
Explanation: It would be this way because if you wrote the triangles out, MW would be in the same place as CD, making them corresponding.
The following segments are corresponding parts of the congruent triangles.
segment MT ≅ segment CA
segment TW ≅ segment AD
segment MW ≅ segment CD
What are congruent triangles?Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.
Given that
Triangle MTW = Triangle CAD
If two triangles are congruent then the corresponding sides and corresponding angles are congruent.
∴ segment MT ≅ segment CA
{corresponding parts of the congruent triangles}
segment TW ≅ segment AD
{corresponding parts of the congruent triangles}
segment MW ≅ segment CD
{corresponding parts of the congruent triangles}
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what are two fractions that equal to 4/6
Answer: 2/3, 8/12
Step-by-step explanation:
Answer:
2/3 and 8/12 (brainlest plssss)
Step-by-step explanation:
Geometry The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.
Answer:
shaded area = 2x² + 6x + 17
If these are squares, what is the "x + 3"?
Step-by-step explanation:
shaded area = (x + 4)² - (x - 1)² = x² + 8x + 16 + x² - 2x + 1 = 2x² + 6x + 17
solve the following equation n-31/105>1
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{n - \dfrac{31}{105}>1}[/tex]
[tex]\large\textsf{First you have to SIMPLIFY EACH SIDES of the INEQUALITY}[/tex]
[tex]\mathsf{n + (-\dfrac{31}{105})>1}[/tex]
[tex]\large\textsf{Second ADD }\mathsf{\dfrac{31}{105}}\large\textsf{ to BOTH of your SIDES}[/tex]
[tex]\mathsf{n - \dfrac{31}{105}+\dfrac{31}{105}> 1 +\dfrac{31}{105}}[/tex]
[tex]\large\textsf{CANCEL out: }\mathsf{-\dfrac{31}{105}+\dfrac{31}{105}}\large\textsf{ because that gives the value of 0}[/tex]
[tex]\large\textsf{KEEP: }\mathsf{1+\dfrac{31}{105}}\large\textsf{ because it helps what is being COMPARED to the n value}[/tex]
[tex]\large\textsf{Simplify above (}\mathsf{1+\dfrac{31}{105}}\large\textsf{) and you should have your result to this question}[/tex]
[tex]\mathsf{1+\dfrac{31}{105}=\bf \dfrac{136}{105}}[/tex]
[tex]\boxed{\mathsf{Answer: \bf n> \dfrac{136}{105\ }\boxed{\large\textsf{ it is an \bf O P E N E D circle shaded to the right}}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please someone help me
Answer:
6,9 and 3 times respectively
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hotel and the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. It takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed).
1. What is the average time a cab must wait for a fare?
2. What is the probability that the line will be full when a cab drives by, causing it to drive on?
Answer:
The appropriate solution is:
(1) 22.81 minutes
(2) 0.171
Step-by-step explanation:
According to the question, the values will be:
The service rate of guess will be:
= [tex]5+3.5[/tex]
= [tex]8.5 \ minutes[/tex]
The mean arrival rate will be:
[tex]\lambda =\frac{60}{5}[/tex]
[tex]=7.5 \ cabs/hr[/tex]
The mean service rate will be:
[tex]\mu= 7.05 \ cabs/hr[/tex]
(1)
The average time a cab must wait will be:
⇒ [tex]W_q=22.95-\frac{1}{7.05}[/tex]
⇒ [tex]=\frac{161.798-1}{7.05}[/tex]
⇒ [tex]=\frac{160.798}{7.05}[/tex]
⇒ [tex]=22.81 \ minutes[/tex]
(2)
The required probability will be:
⇒ [tex]P(X\geq 6)=\frac{1-2.115}{1-7.5}[/tex]
⇒ [tex]=\frac{-1.1115}{-6.5}[/tex]
⇒ [tex]=0.171[/tex]
Looking out from a balcony, the angle of elevation to the top of the next building is
approximately 22 degrees. The angle of depression to the bottom of the building is
approximately 29 degrees. If the building is 200 feet away, how tall is it?
Answer:
191.67 feets
Step-by-step explanation:
From. The attached picture :
Height x can be obtained using trigonometry :
Tan 22 = x / 200
0.4040262 = x / 200
x = 0.4040262 * 200
x = 80.805245 feets
For height, y :
Tan 29 = x / 200
0.5543090 = x / 200
y = 0.5543090 * 200
y = 110.86181 feets
Building height = x + y
Building height = 80.805245 + 110.86181 = 191.67 feets
Ginnys team scored 22 points during the first half of a basketball game.Her team scored 39 points during the second half of the game. Ginnys team beat the other team by 8 points. Which expression could be used to find the other teams score
Her team scored a total of 22+39 = 61 points. This is 8 points higher than the other team, so the other team scored 61-8 = 53 points.
As for which expression your teacher wants as the final answer, it will depend on how simplified you want it to be. You could have the following possible answers:
22+39-861-8Other expressions may be possible as well.
Answer:
The answer depends on whether your teacher wants an algebraic expression or an arithmetic expression.
Algebraic might be:
s = g - 8
Arithmetic:
39 + 22 - 8
Step-by-step explanation:
s (score) is the total number of points Ginny's team scored (g) minus 8 because Ginny's team scored 8 more than the other team.
PLS I NEED HELP ASAP!!!!
Answer:
Step-by-step explanation:
180 - ( 37+67) = 180 - 104
= 76°
A research organization reported that 41 percent of adults who were asked to describe their day responded that they were having a good day rather than a typical day or a bad day. To investigate whether the percent would be different for high school students, 600 high school students were randomly selected. When asked to describe their day, 245 students reported that they were having a good day rather than a typical day or a bad day. Do the data provide convincing statistical evidence that the proportion of all high school students who would respond that they were having a good day is different from 0.41 ?
A) No, because the p value is less than any reasonable significance level
B) No, because the pvalue is greater than any reasonable significance level
C) Yes, because the p-value is less than any reasonable significance level
D) Yes, because the pvalue is greater than any reasonable significance level
E) Yes, because the expected value of the number of students who will report having a good day is 246, not 245.
Answer:
B) No, because the p-value is greater than any reasonable significance level
Step-by-step explanation:
H-null: p = 0.41
H-alt: p =/= 0.41
1 proportion Z test
On a calculator: stat + tests + 5
p: .41
x: 245
n: 600
prop: =/= p
This gives a p-value = .934
(standard significance level is .05, so this p-value is much larger)
fail to reject H-null
If the p-value is much larger than 0.41 then the null hypothesis is rejected. Then the correct option is B.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
A research organization reported that 41 percent of adults who were asked to describe their day responded that they were having a good day rather than a typical day or a bad day.
To investigate whether the percentage would be different for high school students, 600 high school students were randomly selected.
When asked to describe their day, 245 students reported that they were having a good day rather than a typical day or a bad day.
Null hypotheses
p = 0.41
Alternative hypotheses
p ≠ 0.41
The p-value will be given as
p-value = 0.934
The p-value is much larger than p.
More about the null hypotheses and alternative hypotheses link is given below.
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Write an inequality comparing 3/4 and 2/4.
Answer:
3/4 > 2/4
Step-by-step explanation:
3/4 = 0.75
2/4 = 0.5
Therefore, 3/4 > 2/4
HELP PLSSSSSSSS I'M LOST PLSSSSSSSSSSSSSSSSSS
Answer:
1. 1/4 or 25/100, .25 and 25%
2. 1/10 or 1/100, .10 and 10%
Step-by-step explanation:
25 cubes out of 100 is 25/100
Simplify to 1/4
if its 25 cubes out of 100 its gonna fill up 25% or .25 of the whole thing
10 cubes out of 100 is 10/100
then simplify to 1/10
other two are obvious lol
If hari buys 20biscuits for Rs 200 and sells it for Rs 100 find the loss
Answer:
hdvbn
Step-by-step explanation:
nfshvjjnmmnjjmbm
how many times does 6 go into 137
Answer: 22 times
Step-by-step explanation: divide 137 by 6
Which of the following is a line in the drawing?
Answer:
JN
Step-by-step explanation:
It is the only segment that does not have a bend.
Consider parallelogram ABCD with vertices A(-6,6), B(0,10), C(2,4), D(-4,0). Classify the parallelogram and select all that apply
ABCD is a square
ABCD is a rectangle
ABCD is a rhombus
ABCD is none of the above
9514 1404 393
Answer:
D. none of the above
Step-by-step explanation:
The sides are different lengths and not at right angles, so the figure is not a rhombus or a rectangle. It is "none of the above."
__
Counting grid squares in the attached figure, we see that one side is the diagonal of a 2×3 rectangle, and the adjacent side is the diagonal of a 1×3 rectangle. This tells you two things: (a) the sides are different length, (b) they are not at right angles to each other. (If the sides were perpendicular, the slopes of the segments would be opposite reciprocals.)
Find the missing side or angle.
Round to the nearest tenth.
A=15°
C= 120°
b=3
c=[? ]
Enter
Given:
[tex]A=15^\circ, C=120^\circ,b=3[/tex].
To find:
The length of side c.
Solution:
According to the angle sum of property of a triangle, the sum of all interior angles of a triangle is 180 degrees.
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
[tex]15^\circ+m\angle B+120^\circ=180^\circ[/tex]
[tex]m\angle B+135^\circ=180^\circ[/tex]
[tex]m\angle B=180^\circ-135^\circ[/tex]
[tex]m\angle B=45^\circ[/tex]
According to the Law of sines,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Using Law of sines, we get
[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\dfrac{3}{\sin 45^\circ}=\dfrac{c}{\sin 120^\circ}[/tex]
[tex]\dfrac{3}{\dfrac{1}{\sqrt{2}}}=\dfrac{c}{\dfrac{\sqrt{3}}{2}}[/tex]
[tex]3\sqrt{2}\times \dfrac{\sqrt{3}}{2}=c[/tex]
On further simplification, we get
[tex]\dfrac{3\sqrt{6}}{2}=c[/tex]
[tex]3.674235=c[/tex]
[tex]c\approx 3.7[/tex]
Therefore, the length of side c is about 3.7 units.
Graph the linear equation q(x)=-3x+1
The linear function q(x) = -3x + 1 is graphed and attached
How to graph the linear functionThe graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows
For x = -20, q(x) = -3 * -20 + 1 = 61
For x = -10, q(x) = -3 * -10 + 1 = 31
For x = 0, q(x) = -3 * 0 + 1 = 1
For x = 10, q(x) = -3 * 10 + 1 = -29
For x = 20, q(x) = -3 * 20 + 1 = -59
Table of values
x y
-20 61
-10 31
0 1
10 -29
20 -59
These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line
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Hurricane Irma knocked a tree down and destroyed a 45 degree section of your
circular fence that has a radius of 22 feet. If you want to replace the fence, how
long would you need the replacement section to be?h
what is 7 divided by 9102
Answer:
[tex] = 9102 \div 7 \\ = 1300.29 \\ [/tex]
Write an expression with 5 terms where one of the terms is a constant of 3
Answer:
Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.
What's the area of the square?
Answer: 18
Step-by-step explanation:
you just times the 4 1/2 4 times
Paulo’s grandfather gave him a collection of 20 coins. Each month Paulo adds 4 coins to his collection. Which inequality can be used to find m, the number of months after starting his collection when Paulo will have more than 50 coins in his collection?
Answer:
[tex]4m+20>50[/tex]
Step-by-step explanation:
Let m represent the amount of months that has passed.
Paulo started out with 20 coins.
Each month, he adds four more coins to his collection.
Therefore, the amount of coins added after m months will be given by 4m.
So, the amount of coins Paulo has total after m months can be given by:
[tex]4m+20[/tex]
We want to know when Paulo will have "more than" 50 coins in his collection. Therefore, we will use the "greater than" sign. Thus, our inequality will be:
[tex]4m+20>50[/tex]
During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes. Based on this relative frequency, how many pars or better could he be expected to make on the remaining 150 holes? Round to the nearest whole number if necessary.
70 pars or better
60 pars or better
65 pars or better
53 pars or better
Dirk will make 70 pars or better.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.
Out of 90 holes, Dirk made par or better on 42 holes.
At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.
Then, Out of 150 holes, Dirk will make par or better on -
(42/90 x 150) holes
(42/90 x 150)
70
Therefore, Dirk will make 70 pars or better.
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the distance around a square room measures 101 feet 7 inches. Estimate the length of each side of the room
Answer:
304.75 inches
Step-by-step explanation:
Total distance = 101 feet 7 inches
Recall :
1 Feet = 12 inches
Total distance in inches = (101 * 12) + 7 = 1219 inches
Perimeter of square = 1219
Sides of a square are always equal
Number of sides = 4
Hence, length of each side = 1219 inches / 4 = 304.75 inches
Find the surface area of this box in square inches.
Use the formula : SA= 2lw + 2lh + 2w
L = 18 in
w = 20 in
h = 16 in
Find the surface area of the box.
Use the Formula: SA=2lw+2lh+2wh
L= 10.5 in
W= 15.5 in
H= 20 in
Step-by-step explanation:
1.
Given that,
L = 18 in , w = 20 in , h = 16 in
The surface area of the box is given by :
SA= 2lw + 2lh + 2wh
Put all the values,
SA= 2lw + 2lh + 2wh
= 2(lw+lh+wh)
= 2(18(20)+18(16)+20(16))
= 2 (968)
= 1936 in²
2.
L= 10.5 in , W= 15.5 in , H= 20 in
The surface area of the box is given by :
SA= 2lw + 2lh + 2wh
Put all the values,
SA= 2lw + 2lh + 2wh
= 2(lw+lh+wh)
= 2(10.5(15.5)+10.5(20)+15.5(20))
= 2 (682.75)
= 1365.5 in²
Hence, this is the required solution.
PLSS HELP
A given line has the equation 2 x + 12 y = -1.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the
point (0, 9)?
Oy= - 6x + 9
=-*x+9
Oy
Ov=hx+9
O y=6x +9
Save and Exit
Next
Submit
Answer:
B
Step-by-step explanation:
mrk me brainliest plz
The equation of the straight line in slope - intercept form that
is perpendicular to the given line and passes through the point (0, 9) is -
y = 6x + 9.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
where -
{m} is the slope of the line.
{c} is the {y} - intercept.
Given is that the equation of a straight line as -
2x + 12y = - 1
Assume that the equation of the straight line in slope - intercept form as
y = mx + c
Now, the given straight line is perpendicular to the given line. So, we can write the slope as -
{m} = -1/(-1/6)
{m} = 6
For the {y} intercept, we can write -
{c} = 9
So, we can write the equation of the straight line in slope - intercept form that is perpendicular to the given line and passes through the point (0, 9) is -
y = 6x + 9
Therefore, the equation of the straight line in slope - intercept form that
is perpendicular to the given line and passes through the point (0, 9) is -
y = 6x + 9.
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In November, the Sport Shop sold
74 pairs of snow skis and 3 pairs of water
skis. Each month the shop sold 11 more
pairs of water skis and 6 fewer pairs of
snow skis than the previous month,
When was the first month the shop sold
more water skis than snow skis?
Answer:
March is the first month
Step-by-step explanation:
If we make a graph. We can see that the quantity of sold water skis overpasses the quantity of snow skis in the month of March.
3. Mia has read 27 pages out of an 80 page book. What percent of the pages has she read?
Answer: She has read 33.75% of the pages.
Explanation: You can divide 27 by 80 to get the answer :)