Answer:
a) The area to the left of 18 is 0.5.
b) The area to the left of 14 is if 0.309.
c) The area to the right of 17 is of 0.55.
d) The area to the right of 19 is of 0.45.
e) The area between 14 and 30 is of 0.624.
Step-by-step explanation:
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, which is the area to the left of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X, which is the area to the right of X.
A variable is normally distributed with mean 18 and standard deviation 8
This means that [tex]\mu = 18, \sigma = 8[/tex]
a) Find the area to the left of 18.
This is the pvalue of Z when X = 18.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 18}{8}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5.
So the area to the left of 18 is 0.5.
b) Find the area to the left of 14.
This is the pvalue of Z when X = 14. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14 - 18}{8}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.309
The area to the left of 14 is if 0.309.
c) Find the area to the right of 17.
This is 1 subtracted by the pvaleu of Z when X = 17. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17 - 18}{8}[/tex]
[tex]Z = -0.125[/tex]
[tex]Z = -0.125[/tex] has a pvalue of 0.45
1 - 0.45 = 0.55
The area to the right of 17 is of 0.55.
d) Find the area to the right of 19.
This is 1 subtracted by the pvaleu of Z when X = 19. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 18}{8}[/tex]
[tex]Z = 0.125[/tex]
[tex]Z = 0.125[/tex] has a pvalue of 0.55
1 - 0.55 = 0.45
The area to the right of 19 is of 0.45.
e) Find the area between 14 and 30.
This is the pvalue of Z when X = 30 subtracted by the pvalue of Z when X = 14.
X = 30
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 18}{8}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.933
From b), when X = 14, Z has a pvalue of 0.309.
0.933 - 0.309 = 0.624
The area between 14 and 30 is of 0.624.
The area to the left of 18 is 0.5, the area to the left of 14 is 0.309, the area to the right of 17 is 0.55, the area to the right of 19 is 0.45, and the area between 14 and 30 is 0.624.
Given :
A variable is normally distributed with a mean of 18 and a standard deviation of 8.
a) Use the z score formula in order to determine the area to the left of 18.
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm Z = \dfrac{18-18}{8}=0[/tex]
For the z = 0 the p-value is 0.5.
Therefore, 0.5 is the area to the left of 18.
b) Use the z score formula in order to determine the area to the left of 14.
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm Z = \dfrac{14-18}{8}=-0.5[/tex]
For the z = -0.5 the p-value is 0.309.
Therefore, 0.309 is the area to the left of 14.
c) Use the z score formula in order to determine the area to the right of 17.
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm Z = \dfrac{17-18}{8}=-0.125[/tex]
For the z = -0.125 the p-value is 0.45.
Therefore, the area to the left of 17 is given by:
= 1 - 0.45 = 0.55
d) Use the z score formula in order to determine the area to the right of 19.
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm Z = \dfrac{19-18}{8}=0.125[/tex]
For the z = 0.125 the p-value is 0.55.
Therefore, the area to the left of 19 is given by:
= 1 - 0.55 = 0.45
e) Use the z score formula in order to determine the area between 14 and 30.
At X = 30 the z score becomes:
[tex]\rm Z = \dfrac{X-\mu}{\sigma}[/tex]
[tex]\rm Z = \dfrac{30-18}{8}=1.5[/tex]
For the z = 1.5 the p-value is 0.933.
For the z = -0.5 the p-value is 0.309.
Therefore, the area to the left of 14 is given by:
= 0.933 - 0.309
= 0.624
For more information, refer to the link given below:
https://brainly.com/question/13299273
Milo wants to put a fence around the dog park near his house. He measures the sides and finds they are 7 m and 8 m long. He multiplies 7×2 and 8×2 and finds he needs 30 m of fencing.
Which measurement does 30 m?
Choose 1 answer:
(Choice A)
Perimeter
(Choice B)
Length
(Choice C)
Area
Answer:
(Choice A) Perimeter
Step-by-step explanation:
It can't be the length, because it states in the question that the length is 7 m
and it can't be the area because lw = 7(8) = 56 is the area.
What is the value of log, 81?
2
3
4
5
Answer:
log 81 = 1.90849
Step-by-step explanation:
log 81 = log 9^2 = 2 log 9 = 2(0.95424) = 1.90849
Can someone please help me with this ?
PLEASE HELP ME I AM GIVING 30 POINTS PLEASEEE
A 21 inch TV costs $150. It is advertised on sale for 32% off. What is the cost savings? Solve using two different methods.
Answer:
$48 in savings
Step-by-step explanation:
1.
150-(150*32%)=102
150-102=48
2.
30% of 150 is 45
2% of 150 is 3
45 plus 3 is 48
Please brainliest! I did both methods and explained!
THIS IS 7TH GRADE MATH SO ITS EASY
Answer:
b
Step-by-step explanation:
How do you solve for 4-9i/-6i
Answer:
6i
Step-by-step explanation:
If f(x) = 3x + 5, find f(2).
f(2) = ?
Answer:
[tex]3 \times 2 + 5 = 6 + 5 = 11[/tex]
A pair of flip flops is $30. How much will they cost after a 20% discount and 6.5% tax?
Answer:
$6.39
Step-by-step explanation
well, 20% of $30 is $6, so then you just have to add on the tax, which is 39 cents, coming to $6.39
Answer:
25.56
Step-by-step explanation:
30 divided by 4 is 6 so 30- 6=24
6.5% of 24=1.56 sooooo 24+1.56=25.56
Find the surface area of the cone.Use 3.14 for pi and round your answer to the nearest hundredth
Answer:
145.0 cm^2
Step-by-step explanation:
Given data
r= 4cm
l= 5cm
h=??
Apply Pythagoras theorem to find h we have
h^2= 4^2+5^2
h^2= 16+25
h^2= 41
h=√41
h= 6.4cm
Substitute into the formula for the surface area of cone
A=πr(r+√h^2+r^2)
A=3.14*4(4+√6.4^2+4^2)
A=12.56(4+√40.96+16)
A=12.56(4+√56.96)
A=12.56(4+7.547)
A=12.56*11.547
A=145.0 cm^2
The area of the state of Nevada can be estimated using a trapezoid. Estimate the area of the state of Nevada.
A. 31,672 mi2
B. 78,980 mi2
C. 110,622 mi2
D. 131,327 mi2
Answer: 31,672 mi2
Step-by-step explanation:
The area of the state of Nevada can be estimated using a trapezoid
Which expression is equivalent (With explanation)
Answer:
log_7(6)
Step-by-step explanation:
log_7(2)+log_7(3)
log_7(2×3)
log_7(6)
Find the 9th term of the geometric sequence 5, -25, 125, ...
9514 1404 393
Answer:
1,953,125
Step-by-step explanation:
The first term is a1 = 5; the common ratio is r = -25/5 = -5. The generic term is ...
an = a1×r^(n-1)
an = 5×(-5)^(n-1)
So, the 9th term is ...
a9 = 5×(-5)^(9-1) = 1,953,125
How much wire is needed to fence a rectangular garden with measurements 20mmx25m
Answer:
500000mm
Step-by-step explanation:
First to have to convert the meters into millimeters (25mm×1000mm=25000mm) than you have to times the answer by 20 (25000mm×20mm=500000mm) and your answer is 500000mm
Find the value of x and the measure of the missing angle 66 x 40
Answer:
66x40
Step-by-step explanation:
Answer:
x= 180 - (66+40)= 74
I will give brainlest if you answer correctly
I hope this helped
Since it's a cube all sizes are equal
13.5 X 13.5 x 13.5 =
2460.365 m3
Answer:
3.375m^3
Step-by-step explanation:
Given surface area
=13.5m^2
[tex]6a^{2} =13.5m^{2} \\\\a^{2} =\frac{13.5}{6} =2.25\\\\a=\sqrt{2.25}=1.5m\\\\a^{3} =(1.5)^{3} \\\\=3.375 m^{3}[/tex]
hope it helps...
have a great day!!
The dot plots show the number of hours a lightbulb lasts from two different brands. Brand A. Number of hours per lightbulb 1000 4200 1400 1500 1800 2000 Brand B Number of hours per lightbulb .. 1200 1400 1600 1800 2000 Which of the following statements is correct? A. There were more lightbulbs in the dot plot for brand B than in the dot plot for brand A. B. The mean for brand A is the same as the mean for brand B. C. The mean for brand A is higher than the mean for brand B. D. The mean for brand B is higher than the mean for brand A.
Answer:
Step-by-step explanation:
The mean for brand A is higher than the mean for brand B
The mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have:
For brand A:
The number of hours per lightbulb:
1000, 4200, 1400, 1500, 1800, 2000
Mean for brand A:
[tex]\rm Mean(A) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]
[tex]\rm Mean(A)= \frac{1000+4200+1400+1500+1800+ 2000}{6}[/tex]
[tex]\rm Mean(A)= \frac{11900}{6}\\\\\rm Mean(A) = 1983.33[/tex]
For Brand B:
The number of hours per lightbulb:
1200, 1400, 1600, 1800, 2000
Mean for brand B:
[tex]\rm Mean(B) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]
[tex]\rm Mean(B)= \frac{1200 +1400 +1600 +1800 +2000}{6}[/tex]
[tex]\rm Mean(B)= \frac{8000}{5}\\\\\rm Mean(B) = 1600[/tex]
We can see that:
Mean(A) > Mean(B)
Thus, the mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.
Learn more about the mean here:
https://brainly.com/question/22871228
Find angle x to the nearest tenth.
47
73
78
A) 36.1
B) 66.2
C) 26.3
D) 31.6
$1,200 Is Invested in two different accounts paying 6% and 8% Interest. If a total of $81 Interest is earned after one year,
then how much money was Invested at 8%?
$1,200
$750
$450
$800
Answer:
It would be A
Step-by-step explanation:
C. A musician had 1.2 x 102
fans at his very first show
ever played. Six years later,
84,000 people were at his
show. How many times more
people were at his most recent
show compared to the very
first show he played?
Answer:
688 people
Step-by-step explanation:
A man is three times as old as his daughter. If the difference in their ages is 36 years, find the ages of the father and daughter.
Answer:
man's age = 54
daughter's age = 18
Step-by-step explanation:
x = man's age
y = daughters age
x = 3y
x - y = 36
substitute for x:
3y -y = 36
2y = 36
y = 18
x = 54
If a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.
What is an equation?Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation. The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation.
It is given that, A man is three times as old as his daughter. If the difference in their ages is 36 years,
We have to find the ages of the father and daughter.
Suppose the age of the father and daughter will be x and y respectively.
If the man is three times as old as his daughter,
x = 3y
If the difference in their ages is 36 years
x - y = 36
Put the value of x as,
3y -y = 36
2y = 36
y = 18
x = 54
Thus, if a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.
.Learn more about the equation here,
https://brainly.com/question/10413253
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Alternate exterior angles are congruent which angle forms a pair of alternate exterior angles with angle 2?
What is the distance between (-4, 8) and (12, 8) on the coordinate plane? A 16 units B 8 units C 0 units D 4 units
Answer:
16 units
Step-by-step explanation:
We need to find the distance between (-4, 8) and (12, 8) on the coordinate plane.
We know that the distance between two points on the coordinate plane is given by :
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Put x₁ = -4, x₂ = 12, y₁ = 8 and y₂ = 8
So,
[tex]D=\sqrt{(12-(-4))^2+(8-8)^2}\\\\=16\ units[/tex]
So, the distance between the two points is equal to 16 units.
what is the answer to x+2=17-4x
Answer:
x = 3
Step-by-step explanation:
Move all terms containing x to the left
5x + 2 = 17
Move all terms not containing x to the right
5x = 15
Divide each term by 5 and simplify
x = 3
This is my last assignment, pls help
16 minutes= 6 bushes trimmed
how many minutes would it take for 30 bushes to be trimmed?
6 1/4 quarts =___ pints?
Answer:12.5
Step-by-step explanation:
Answer:
12.5 pints
Step-by-step explanation:
what are the features of the quadratic function f(×) =×2 +10×+21?
A is the correct answer
Or
Vertex = (-5,-4), y-intercept = (0,21), x-intercepts = (-7,0) and (-3,0), axis of
symmetry is x = -5
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answer:
Volume of a cylinder (V) : π x radius ² x height
V = 3.14 x 12² x 13
V = 5878.08 cubic millimeters.
Step-by-step explanation:
Suppose a jar contains 12 red marbles and 18 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer in decimal form, rounded to the nearest thousandth.
Evaluate the following expression 6 ^-3
Answer:
1/216
Step-by-step explanation:
Answer:
Exact form = 1/216.
Decimal form = 0.004629
i will give lots of points for these 4 answers
Answer:
1&3 are wrong 4 and 2 are right
Step-by-step explanation:
may i be marked brainliest