Answer:
(0.1361 ; 0.2239)
Step-by-step explanation:
n1 = 1400 ; p1 = 0.50 ; n2 = 1320 ; p2 = 0.38
Confidence interval = mean ± margin of error
Mean = p1 - p2
Point estimate :
p1 - p2 = 0.50 - 0.38 = 0.18
Margin of Error (MOE) = Zcritical * S. E
Standard Error(S. E) :
Sqrt[(p1(1-p1)/n1) + (p2(1-p2)/n2)]
(p1(1-p1)/n1) = 0.50(0.50) / 1400 = 0.0001785
(p2(1-p2)/n2) = 0.38(0.62) / 1320 = 0.0001784
S. E = sqrt(0.0001785 + 0.0001784)
S. E = sqrt(0.0003569)
S. E = 0.0188917
Zcritical at 98% = 2.326
MOE = Zcritical * S. E
MOE = 2.326 * 0.0188917
MOE = 0.0439420942
MOE = 0.0439
Confidence interval = mean ± margin of error
Confidence interval = 0.18 ± 0.0439
Lower boundary = (0.18 - 0.0439) = 0.1361
Upper boundary = (0.18 + 0.0439) = 0.2239
(0.1361 ; 0.2239)
a company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. suppose the probability distribution of the lifetimes of the participants in the plan is approximately normal with mean equal to 66.3 years and standard deviation equal to 3.6 years. nine participants are randomly selected. what is the probability that the average age at death of these nine participants will exceed 68 years
Answer:
0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 years
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 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.
Approximately normal with mean equal to 66.3 years and standard deviation equal to 3.6 years.
This means that [tex]\mu = 66.3, \sigma = 3.6[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{3.6}{\sqrt{9}} = 1.2[/tex]
What is the probability that the average age at death of these nine participants will exceed 68 years?
This is 1 subtracted by the pvalue of Z when X = 68. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68 - 66.3}{1.2}[/tex]
[tex]Z = 1.42[/tex]
[tex]Z = 1.42[/tex] has a pvalue of 0.9222
1 - 0.9222 = 0.0778
0.0778 = 7.78% probability that the average age at death of these nine participants will exceed 68 years
Olivia has 2 gallons and 3 quarts of vanilla ice cream and 1 gallon and 2 quarts of chocolate ice cream left over from a party What is the total number of gallons and quarts of ice cream that Olivia has left over?
Answer:
4 gallons 1 quart total ice cream
first you add the gallons and the quarts.
so, 2 gallons vanilla + 1 gallon chocolate is 3 gallons.
3 quarts vanilla + 2 quarts chocolate is 5 quarts.
4 of the 5 quarts are taken to make up another gallon.
so the answer is 4 gallons 1 quart total ice cream.
Silas brought an ice chest to the picnic. A model of the ice chest is shown below . 15in Width, 30 inches length, and 15 inches height. What is the volume, in cubic inches of the ice chest?
Answer:
6,750 in.³
Step-by-step explanation:
The ice chest is a rectangular prism or a cuboid.
Volume of the ice chest = volume of rectangular prism = l*w*h
Where,
l = 30 in.
w = 15 in.
h = 15 in.
Volume = 30*15*15 = 6,750 in.³
if f(x) =2((x)), find f(-1/4)
Answer:
Combine
f and 1/4.
and u get - f/4
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
2(-1/4)
Pls helppp I don’t understand also if you can can you show the works pls if you can tho
Answer:
I would help but it is just black try to repost it and i will tell you what it is
Step-by-step explanation:
Graph the inequality on a grid which resembles the image. 400x + 4y < 2000
Answer:
te awnser is
Step-by-step explanation:
For every quarter spent, Reggie receives 75 food pebbles to feed the fish at a hatchery. Reggie has thrown 600 food pebbles into the fish pools. How many quarters did Reggie spend at the hatchery?
Answer:
8
Step-by-step explanation:
What is the value of p in the equation
8p +2 = 4p - 102
1) 1
2) -1
3) 3
4) -3
Answer:
-26
Step-by-step explanation:
sorry but from my calculations I didn't get any of the options I got -26
Help me out thanks !!!!!
Answer:
B) ∠SBY = 117°
Step-by-step explanation:
interior angles in a pentagon = (5x180) - 360 = 540°
each angle = 540/5 = 108°
interior angles in a octagon = (8x180) - 360 = 1080°
each angle = 1080/8 = 135°
∠SBY = 360 - 108 - 135 = 117°
Point KK is located at (5,-4)(5,−4) on the coordinate plane. Point KK is reflected over the xx-axis to create point K'K
What ordered pair describes the location of K'?K
Answer:
The ordered pair that describes the location of K' is (5,4).
Step-by-step explanation:
Reflection over the x-axis:
When a point is reflected over the x-axis, it's x-coordinate stays the same, while the signal of the y-coordinate is changed. So
(x,y) -> (x,-y)
In this question:
Point K(5,-4)
Reflection over the x-axis:
(5,-4) -> (5,-(-4)) -> (5,4)
The ordered pair that describes the location of K' is (5,4).
(fractions) 3/4 + 1/5
Answer:
19/20
Step-by-step explanation:
write all numerators above the least common denominator 20
15+4/20
add the numbers
19/20
Answer: 19/20
Step-by-step explanation:
Find your common denominator
3/4
Multiply by 5
15/20
1/5
Multiply by 4
4/20 + 15/20= 19/20
Hope this helped :)
find the area of the triangle
Answer:
Step-by-step explanation:
You know two sides and the angle between them. Use the Law of Cosines to find the third side.
q = √(p²+r²-2pr·cosQ) ≅ 8.533 units
Use Heron's formula to find area
semi-perimeter s = (p+q+r)/2 ≅ 10.317 units
area = √(s(s-p)(s-q)(s-r)) ≅ 16.3 units²
Help on question 5 please :))
Answer:
the answer is I LIKE YOUR CUT G
Step-by-step explanation:
your a bot at fortnite
Answer:
b. Substitute 8x+4 for y in the first equation.
-7( 2y - 3x + 9 ) =
Plz help
Answer:
21x - 14y - 63
Step-by-step explanation:
Rearrange the terms so it's: -7(-3x + 2y + 9)
Then distribute it and you have your answer, unless you know what x and y are
what is 9^7 written in expanded form
Answer:
9*9*9*9*9*9*9
Step-by-step explanation:
it's basically 9 multiply by itself for 7 times
Please find the circumference, will give brainliest!
Answer:
43.96
Step-by-step explanation:
Hi. I need help with math. 8th grade.
Answer:
260 is the answer. jjrjejjehene
Based on the scatterplot below what is the most likely value for pounds of apples phone number of Apples is 60
You and three friends order a large pizza and three sodas at Blue Mountain Pizza.
- The sub total is 32.85.
- There is a 7% sales tax
- You want to leave an 18% tip on the price of the meal plus tax.
If the bill is divided evenly how much will each person pay? (Round to the nearest cent)
Please show work!
Answer:
$13.20
Step-by-step explanation:
7% = 0.7 so you add that to $32.85 = $33.55
18% of $33.55 is 6.039 so you add that to $33.55 = 39.589
That is the total of the bill so you divide it by 3
39.589 /3 =13.1963
rounded to the nearest cent is $13.20
can someone help me please
Answer:
i think its b
Step-by-step explanation:
How to get 10 with the numbers 7, 11, 4 and 2 in that order?
Answer:
Huh!! What is this question supposed to mean?
write
[tex] \frac{12}{25?} [/tex]
as a decimal and as a percent
A flagpole is 4 meters tall. How many
centimeters tall is the flagpole?
Answer:
400 cm
Step-by-step explanation:
100 centimeters in a meter.
4 * 100 = 400
help me with this thank you
Answer: think it’s c 4/28
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
A group of 20 students attempting a MathematicalChallenge have an average age of 11. When their teacher is included their average age is12. What is the age of the teacher?
Answer:
32.
1st get the total age of the students
x/20 = 11
x=11x20
x =220 (total age of students)
add y ( teachers age) to the equation
(220 + y)/21=12
y= 32
Answer:
32
Step-by-step explanation:
20 * 11= 220
21 * 12= 252
252-220=32
2/5 x 30 pls help me
Answer:
12
Step-by-step explanation:
Answer:
The answer is 12.
PLEASE HELP I WILL GIVE BRAINLIEST IF YOU GET IT RIGHT 7TH GRADE MATHH
Answer:
990
Step-by-step explanation:
(21*18*2)+(21*3*2)+(18*3*2)
=990
yo momma is 600 pounds she eats 300 more pounds of food and gets fatter how many more pounds does she need to get to weigh 3000 pounds
Answer:
2100
Step-by-step explanation:
L M A O
A rectangular balcony is 10 feet long and 4 feet wide. What is its area?
The same survey database cited in exercise 4.3.1 (A-5) shows that 32 percent of U.S. adults indicated that they have been tested for HIV at some point in their life. Consider a simple random sample of 15 adults selected at a time. Let X be the number of adults who have been tested for HIV in the sample. For the following, find the numerical answer and describe the answer in words:
a. Three
b. Between five and nine, inclusive
c. More than five, but less than 10
d. Six or more
e. Less than five
f. Find the mean and the variance of the number of people tested for HIV in samples of size 15.
Answer:
a. P(X = 3) = 0.145736
b. P(5≤X≤9) = 0.5462
c. P(5<X<10) = 0.3332
d. P(X≥6) = 0.3393
e. P(X<5) = 0.4477
f. Mean = 4.8, Variance = 3.264
Step-by-step explanation:
Given - The same survey database cited in exercise 4.3.1 (A-5) shows
that 32 percent of U.S. adults indicated that they have been
tested for HIV at some point in their life. Consider a simple
random sample of 15 adults selected at a time. Let X be the
number of adults who have been tested for HIV in the sample.
To find - For the following, find the numerical answer and describe
the answer in words:
a. Three
b. Between five and nine, inclusive
c. More than five, but less than 10
d. Six or more
e. Less than five
f. Find the mean and the variance of the number of people
tested for HIV in samples of size 15.
Proof -
Given that , n = 15, p = 32% = 0.32
Now,
a.
P(X = 3) = binomial distribution (3, 15, 0.32, 0)
= [tex]\left(\begin{array}{ccc}15\\3\end{array}\right)(0.32)^{3}(1-0.32)^{15 - 3}[/tex]
= 455(0.032768)(0.009774)
= 0.145736
⇒P(X = 3) = 0.145736
b.
P(5≤X≤9) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= [tex]\left(\begin{array}{ccc}15\\5\end{array}\right)(0.32)^{5}(1-0.32)^{15 - 5}[/tex]+ [tex]\left(\begin{array}{ccc}15\\6\end{array}\right)(0.32)^{6}(1-0.32)^{15 - 6}[/tex] + [tex]\left(\begin{array}{ccc}15\\7\end{array}\right)(0.32)^{7}(1-0.32)^{15 - 7}[/tex] + [tex]\left(\begin{array}{ccc}15\\8\end{array}\right)(0.32)^{8}(1-0.32)^{15 - 8}[/tex]+ [tex]\left(\begin{array}{ccc}15\\9\end{array}\right)(0.32)^{9}(1-0.32)^{15 - 9}[/tex]
= 0.213 + 0.1671 + 0.1011 + 0.0476 + 0.0174
= 0.5462
⇒P(5≤X≤9) = 0.5462
c.
P(5<X<10) = + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= [tex]\left(\begin{array}{ccc}15\\6\end{array}\right)(0.32)^{6}(1-0.32)^{15 - 6}[/tex] + [tex]\left(\begin{array}{ccc}15\\7\end{array}\right)(0.32)^{7}(1-0.32)^{15 - 7}[/tex] + [tex]\left(\begin{array}{ccc}15\\8\end{array}\right)(0.32)^{8}(1-0.32)^{15 - 8}[/tex]+ [tex]\left(\begin{array}{ccc}15\\9\end{array}\right)(0.32)^{9}(1-0.32)^{15 - 9}[/tex]
= 0.1671 + 0.1011 + 0.0476 + 0.0174
= 0.3332
⇒P(5<X<10) = 0.3332
d.
P(X≥6) = 1 - P(X < 6)
= 1 - P(X ≤ 5)
= 1 - binomial(5, 15, 0.32, 1)
= 1 - 0.6607
= 0.3393
⇒P(X≥6) = 0.3393
e.
P(X<5) = P(X≤4)
= binomial (4, 15, 0.32, 1)
= 0.4477
⇒P(X<5) = 0.4477
f.
Mean = np
= 15(0.32)
= 4.8
⇒Mean = 4.8
Variance = np(1-p)
= 15(0.32)(1 - 0.32)
= 4.8(0.68)
= 3.264
⇒Variance = 3.264