Answer:
a) 0.0016 = 0.16% probability that the sample mean is at least $30.00.
b) 0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00
c) 90% of sample means will occur between $26.1 and $28.9.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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 = 27.50, \sigma = 7, n = 68, s = \frac{7}{\sqrt{68}} = 0.85[/tex]
a. What is the likelihood the sample mean is at least $30.00?
This is 1 subtracted by the pvalue of Z when X = 30. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem, we have that:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 27.5}{0.85}[/tex]
[tex]Z = 2.94[/tex]
[tex]Z = 2.94[/tex] has a pvalue of 0.9984
1 - 0.9984 = 0.0016
0.0016 = 0.16% probability that the sample mean is at least $30.00.
b. What is the likelihood the sample mean is greater than $26.50 but less than $30.00?
This is the pvalue of Z when X = 30 subtracted by the pvalue of Z when X = 26.50. So
From a, when X = 30, Z has a pvalue of 0.9984
When X = 26.5
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{26.5 - 27.5}{0.85}[/tex]
[tex]Z = -1.18[/tex]
[tex]Z = -1.18[/tex] has a pvalue of 0.1190
0.9984 - 0.1190 = 0.8794
0.8794 = 87.94% probability that the sample mean is greater than $26.50 but less than $30.00.
c. Within what limits will 90 percent of the sample means occur?
Between the 50 - (90/2) = 5th percentile and the 50 + (90/2) = 95th percentile, that is, Z between -1.645 and Z = 1.645
Lower bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = -1.645*0.85[/tex]
[tex]X = 26.1[/tex]
Upper Bound:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.645 = \frac{X - 27.5}{0.85}[/tex]
[tex]X - 27.5 = 1.645*0.85[/tex]
[tex]X = 28.9[/tex]
90% of sample means will occur between $26.1 and $28.9.
I need help with this shi
One-third x + one-sixth y = 2. When x is 3, 1 x + StartFraction 3 Over 6 EndFraction y = 6. One-half x + three-fourths y = negative 3. When x is negative 2, negative 1 x minus StartFraction 6 Over 4 EndFraction = 6. Negative 1 y = 12.
Continue solving the system of equations.
What is the solution to the system?
(
,
)
Answer:
(12, -12)
Step-by-Step:
I got it right on Edge 2021
Answer:
its 12,-
12
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Select all of the following tables which represent y as a function of x.
Answer:
the second and third one
Step-by-step explanation:
two y's that are the same can't have 2 outcomes
Help me please! I am in desperate need
Answer:
C. The coefficients of [tex]x^ay^b[/tex] and [tex]x^by^a[/tex] are equal.
Step-by-step explanation:
The binomial theorem is given as:
[tex](x+y)^n=\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k[/tex]
[tex]n-k+k=n[/tex], and the coefficient of these terms are represented by [tex]\binom{n}{k}[/tex].
*Note [tex]\binom{n}{k}=\binom{n}{n-k}=\frac{n!}{k!(n-k)!}[/tex]
Therefore the coefficients of [tex]x^ay^b[/tex] and [tex]x^by^a[/tex] are equal.
Part2
Please help I’ll make u brainly
Answer:
someone game me that same question but sadly i wasn't able to get the answer sorry for the inconvience
Step-by-step explanation:
Answer:
3. 2nd degree. Leading term:
[tex] {3x}^{2} [/tex]
Leading coefficient: 3x
Part 1:
[tex] {2x}^{2} + 11x + 15[/tex]
Part 2:
[tex] {3x}^{2} - x - 2[/tex]
Part 3:
[tex] - {x}^{2} + 12x + 17[/tex]
(Part 3 should be correct, double check it, I think it cancels out the minuses in the part 2 equation?)
P.S. I forgot to solve the equations on this and the first page, don't forget that and I can leave another answer for those if you need!
Solve the triangle given that a=19 b=16, c=11.
Answer:
The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.
Step-by-step explanation:
From statement we know all sides of the triangle ([tex]a[/tex], [tex]b[/tex], [tex]c[/tex]), but all angles are unknown ([tex]A[/tex], [tex]B[/tex], [tex]C[/tex]). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.
If we know that [tex]a = 19[/tex], [tex]b = 16[/tex] and [tex]c = 11[/tex], then the missing angles are, respectively:
Angle A
[tex]a^{2} = b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A[/tex] (1)
[tex]A = \cos^{-1}\left(\frac{b^{2}+c^{2}-a^{2}}{2\cdot b\cdot c} \right)[/tex]
[tex]A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right][/tex]
[tex]A \approx 87.395^{\circ}[/tex]
Angle B
[tex]b^{2} = a^{2}+c^{2}-2\cdot a\cdot c \cdot \cos B[/tex] (2)
[tex]B = \cos^{-1}\left(\frac{a^{2}+c^{2}-b^{2}}{2\cdot a\cdot c} \right)[/tex]
[tex]B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right][/tex]
[tex]B\approx 57.271^{\circ}[/tex]
Angle C
[tex]C = 180^{\circ}-A-B[/tex]
[tex]C = 180^{\circ}-87.395^{\circ}-57.271^{\circ}[/tex]
[tex]C = 35.334^{\circ}[/tex]
The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.
PRE CALC HELP!!! 100 PTS AND BRAINLIEST
(the one I chose isn't correct I just accidentally pressed it)
Hello!
[tex]\large\boxed{\frac{\pi }{4} < x < \frac{5\pi }{4}}[/tex]
To begin, we can solve the inequality:
sin(x) > cos(x)
Divide both sides by cos(x):
sin(x) / cos(x) > 1
tan(x) > 1
x > π/4
However, we can also solve it the other way to produce the end to the interval:
sin(x) > cos(x)
1 > cot(x)
x < 5π/4
Therefore, sin(x) > cos(x) on the interval π/4 < x < 5π/4.
Answer:
π/4 < x < 5π/4.
Find the measure of angle B
(9x+2) (5x-4)
Answer:
119
Step-by-step explanation:
[tex]due \: to \: Corresponding \: angles \\ (5x - 4) + (9x + 2) = 180 \\ 14x = 182 \\ x = 13 \\ \\ 9.13 + 2 = b \\ b = 119[/tex]
Answer:
In the given figure, we know that (angle B+angle C)=180°.
[tex](9x + 2) + (5x - 4) = 180 \\ 14x - 2 = 180 \\ 14x = 182 \\ \boxed{x = 13}[/tex]
Angle B = (9x+2) = (9×13+2) = (117+2) = 119°.
Ted's taxi service has cabs that can seat 4 people and vans that can seat 15 people. The taxi service can transport a maximum of 134 people in its 17 units. How many vans does Ted's Taci Service have in it's fleet?
A. 19
B. 11
C. 9
D. 6
Answer:
D. 6
Step-by-step explanation:
Please help me with my homework!
Linda used a number line to simplify an expression. Which expression did Linda simplify based on the number line?
A. -9+1
B. -1-9
C. -1+(-8)
D. -1-(-8)
If a leaky faucet drips one ounce of water per minute approximately how many gallons per day is that
Answer:
Step-by-step explanation:
1hr=60mins
24hrs in a day
1hr=60oz
60oz x 24hrs =1440 oz
1440oz = 11.25gal
PLEASE MARK BRAILIEST
Harper knows he is 50 yards from school. The map on his phone shows that the school is 34 inch from his current location.
How far is Harper from home, if the map shows the distance as 3 inches?
Kendrick walked of a mile in of an hour. How fast did he walk? _____miles per hour
Answer:
He walked at 1 mile per hour
Step-by-step explanation:
Answer:
He walked at 1 mph
Step-by-step explanation:
Add the expression. Write the sum in simplest form 3 /x+2 + x+1 / x^2 + 5x + 6
Answer: ?
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\frac{3}{x+2} +\frac{x+1}{x^2+5x+6} \\=\frac{3}{x+2} +\frac{x+1}{x^2+3x+2x+6} \\=\frac{3}{x+2} +\frac{x+1}{x(x+3)+2(x+3)} \\=\frac{3}{x+2} +\frac{x+1}{(x+3)(x+2)} \\=\frac{3(x+3)+x+1}{(x+3)(x+2)} \\=\frac{3x+9+x+1}{(x+3)(x+2)} \\=\frac{4x+10}{(x+3)(x+2)} \\=\frac{4x+10}{x^2+5x+6}[/tex]
[tex]=\frac{2(2x+5)}{(x+3)(x+2)}[/tex]
In an hyperbola, the fixed points that have a constant difference in distance from the center are called _
A. Asymptotes
B. Centers
C. Foci
D. Vertices
Please select the best answer from the choices provided
OA
OB
OC
OD
The correct answer is C. Foci.
A hyperbola is defined as the flat open curve resulting from the intersection of a right circular cone from a plane not parallel to any of its origins. The line joining the foci of the hyperbola is called the base line.
The perpendicular to the middle of the baseline is called the center line. It becomes apparent that all points of the center line are equidistant from the foci.
Learn more in https://brainly.com/question/15697124
six less than six times a number is 12
Answer:
x = 3
equation: 6x - 6 = 12
Step-by-step explanation:
6x - 6 = 12
aka:
6x + -6 = 12
+6. +6
6x = 18
/6. /6
x = 3
check: 6(3) - 6 = 12
18 - 6 = 12
12 = 12
Find the slope of a line parallel to the line through the points. ises 11.3. omplete the following: (c) (10, 6) and (10, 10)
Answer:
cv vfgvbgfgvd
Step-by-step explanation:
A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a stop (combined with the brakes) after the end of a run. Suppose that the main chute deploys with probability 0 . 95, and that if the main fails to deploy, the backup deploys with probability 0.999.
Required:
a. What is the probability that one of the two parachutes deploys?
b. What is the probability that the backup parachutes deploys?
Answer:
a. 0.99995 = 99.995% probability that one of the two parachutes deploys
b.0.04995 = 4.995% probability that the backup parachutes deploys
Step-by-step explanation:
a. What is the probability that one of the two parachutes deploys?
Either the first deploys(with probability 95%), or the first does not deploy(probability 5%) and the second does(probability 99.9%). So
[tex]p = 0.95 + 0.05*0.999 = 0.99995[/tex]
0.99995 = 99.995% probability that one of the two parachutes deploys
b. What is the probability that the backup parachutes deploys?
The first does not deploy(probability 5%) and the second does(probability 99.9%). So
[tex]p = 0.05*0.999 = 0.04995[/tex]
0.04995 = 4.995% probability that the backup parachutes deploys
How do you write 3% as a fraction
Answer: 3/100
Step-by-step explanation:
Answer:
3/100
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line shown on the graph?
С
a
Find all the missing elements:
B
A = 40°
a = 8
А
b = 7
b
B = [?]° C = [ ]° c = [ ]
Round to the nearest tenth.
C С
Answer:
B=34.2
C=105.8
c=12.0
Step-by-step explanation:
find B using the sine rule
(sin40÷8)=(sinB÷7)
rearrange
sin B= (sin40x7)÷8
sin B=0.562
make sure to use your calculator
then press shift sin to find B
B= 34.2°
to the nearest tenth means to 1 decimal place
sum of angles in a triangle is 180
so 180-(40+34.2)=105.8°=C
use sine rule again to find c
(sin105.8÷c)=(sin40÷8)
rearrange
c= (sin 105.8x8)÷sin40
c=12.0
Help asappppp ? Writing linear Equations?
Answer:
C=0.75m+3
Step-by-step explanation:
3=flat fee
0.75 per mile
m=mile
c=cost
anyone can u please help me? lol
Answer:
-1/30
Step-by-step explanation:
just subtract then divide.
(this is simplest form)
nvm
my bad, i forgot some steps you can delete this answer if wanted.
How to Simplify (7x+2)+(x+8)-2x
Answer:
Step-by-step explanation:
The answer to this should be 2(3x+5)
The simplified answer of this is 6x+10
I hope I helped you out.
Answer:
P: ()
E: 5^4 (example)
M:x
D: ÷
A:+
S:-
can someone help with 9-12 please ?
Answer:
9-12 is -3
Step-by-step explanation:
In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=60°, and JH = 80 feet. Find the length of IJ to the nearest foot.
Answer:
46.2
Step-by-step explanation:
46.188= 46.2
HELP!
What is the scale factor !
Answer:
A scale factor is usually a decimal which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x.
Find the value of X.
All 3 sides of the triangle are the same, which means all 3 inside angles are the same. Each inside angle is 60 degrees.
We now have 3x = 60
Divide both sides by 3:
x = 60/3
x = 20
Answer:
As in the given figure, all the sides are equal i.e., 5 units
It is a equilateral triangle.
In equilateral triangle all the angles are 60°.
[tex]3x = 60 \\ x = \frac{60}{3} \\ \boxed{x = 20}[/tex]
20 is the right answer.please help asap will give brainliest !!!
Step-by-step explanation:
The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
So the smallest angle is <P.
Hope it may help :)
