Using the normal distribution, it is found that:
a) The 65th percentile is of 37.31.
b) The 90th percentile is of 42.68.
c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]Question a:
The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 0.385(6)[/tex]
[tex]X = 37.31[/tex]
The 65th percentile is of 37.31.
Question b:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 1.28(6)[/tex]
[tex]X = 42.68[/tex]
The 90th percentile is of 42.68.
Question c:
The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:
X = 38:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35}{6}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 35}{6}[/tex]
[tex]Z = -1.17[/tex]
[tex]Z = -1.17[/tex] has a p-value of 0.121.
0.6915 - 0.121 = 0.5705.
There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
Question d:
The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 35}{6}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 35}{6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.9332 - 0.8413 = 0.0919
There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
A similar problem is given at https://brainly.com/question/24663213
What is the midpoint of the segment shown below?
10
O A. (6.3)
(2,3)
(10,3)
B. (6,3)
- 10
10
C. (5,3)
-10
D. (533)
SUE
Answer:
b. (6,3)
Step-by-step explanation:
10+2=12
12/2=6
The line is always on 3, so that will be the y coordinate!
The midpoint of the line segment are (6, 3). Therefore, option B is the correct answer.
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x₁+x₂)/2, (y₁+y₂)/2]
From the graph, the coordinate points of ends of line segment are (2, 3) and (10,3).
Here, midpoint = [(2+10)/2, (3+3)/2]
= (6, 3)
Therefore, option B is the correct answer.
To learn more about the formula of midpoint visit:
https://brainly.com/question/4728902.
#SPJ7
A baseball tournament begins with 128 teams. After each round of games, only half of the teams are left. How many teams will be left after four rounds of games?
Answer:
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
answer is 8
can i have help please
Mr. Gooddeal sells cars. He gets to keep 1/6 of his sales commission. How much must he sell in order to earn $1500.
Solve 2^2x-3 = 128. X =
Answer:
x=131/4
Step-by-step explanation:
ANYONE CAN HELP ME ?? :)
Answer:
12[tex]\frac{2}{3}[/tex] cm
Step-by-step explanation:
Have a nice day
O 8) Translate the point and give the resulting coordinates.
(-9,6); (5,-2)
Answer:
- 4/7
Step-by-step explanation:
The resulting point is 5 units right and 2 units down, and the resulting coordinates are (- 4, 4).
Used the concept of coordinate that states,
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
The coordinate is (- 9, 6) and (5, - 2).
Now the value of the resulting coordinate is found as,
(- 9 + 5, 6 - 2)
= (- 4, 4)
Therefore, the resulting point is 5 units right and 2 units down, and the resulting coordinates are (- 4, 4).
To learn more about the coordinate visit:
https://brainly.com/question/24394007
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Find the perimeter. Simplify your answer.
add all the sides!
[side one] + [side two] + [side three]
[7y + 10] + [7y + 10] + [y - 4]
= 14y + 20 + y - 4
= 15y + 16
hope this helps :) !!
Answer:
15y + 16
Step-by-step explanation:
2(7y + 10) + y - 4
14y + 16 + y
15y + 16
Craig wants to create a right triangle with side lengths 4 centimeters, 6 centimeters, and 8 centimeters. Is this possible? Why or why not?
Answer:
It's not possible
Step-by-step explanation:
In right triangle hipotenuse must be the longest side so it'll be 8 and legs will be 4 and 6.
So
[tex]4 {}^{2} + 6 {}^{2} [/tex]
Doesn't equal to
[tex]8 {}^{2} [/tex]
16+36=52 not 64
It takes Billy 40 minutes to drive to his friend's house at his normal speed but it takes two hours if he drives 20 mph slower how far away is Billy's friend's house. How far does his friend live?
Answer:
20 miles
Step-by-step explanation:
Find the constant(s): 12x - 8 - 12
Hello there!
-8 and -12 are constants
A constant is any real number.
Hope this helps!
~Just a determined gal
#CarryOnLearning
[tex]MysteriousNature[/tex]
A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under
the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer in the box to complete the inequality
Answer:
<-2
Step-by-step explanation:
x + 8 less than or equal to 6
3/5 + (-4/11)...........
Answer:
13/55
Step-by-step explanation:
(3/5) + -(4/11) = (3/5) - (4/11) = (33/55) - (20/55) = (13/55)
Tell me if I'm wrong :)
[tex]\dfrac 35 + \left( -\dfrac 4{11} \right) \\\\\\=\dfrac35 - \dfrac{4}{11} \\\\\\=\dfrac{13}{55} \approx 0.24[/tex]
The elevators in an office building have been approved for a maximum load of 3,600 pounds.
Can the elevator hold a weight of exactly 3,600 lbs? If w = weight in elevator, what should the inequality look like?
Plz help thx.
Answer:
w [tex]\leq[/tex] 3,600
Step-by-step explanation:
[tex]\leq[/tex] means less than or equal to.
Write 63 as the product of prime factors
HOW AM I WRONG???
Answer:
It says in ascending order, and I don't think exponents will work.
Step-by-step explanation:
I think the correct answer would be 3 x 3 x 7, or 3² x 7
The only mistake that I can see is that it is not in ascending order.
-Chetan K
Answer:
3*3*7 or 3^2*7
Step-by-step explanation:
Do you need to have the exponent of 2?
If not, then write it as 3*3*7 or 3^2*7
Help I am stuck I will give brainlist
Answer: I think it is B
Step-by-step explanation:
Simplify the exponential expression 48 Superscript one-half.
what is the lateral surface area of a right circular cylinder with height 10cm and base area 154cmsquare (use pi = 22/7)
Answer:
Lateral surface area = 154cm²
Step-by-step explanation:
h = 10cm
pi = 22/7
base area = 154cm²
2πrh = 154cm²
2 × 22/7 × r × 10 = 154
440/7 × r = 154
r = 154 ÷ 440/7 = 2.45
r = 2.45
LSA of right circular cylinder = 2πrh
2 × 22/7 × 2.45 × 10
44/7 × 24.5 = 1078/7
1078/7 = 154
Therefore, lateral surface area = 154cm²
Hope it helps:)
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
d>-7
Step-by-step explanation:
I need help pls I'll give brainliest!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\sqrt{32}[/tex]
Step-by-step explanation:
4^2+ 4^2=c
16+16=32
[tex]\sqrt{32}[/tex]
=5.65685424949
Complete the equation of the line through (-6,-5)(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and (-4,-4)(−4,−4)left parenthesis, minus, 4, comma, minus, 4, right parenthesis.
Use exact numbers.
Answer:
d
Step-by-step explanation:
Answer:
Hint #33 / 3
The equation is y=\dfrac{1}{2}x -2y=
2
1
x−2y, equals, start fraction, 1, divided by, 2, end fraction, x, minus, 2.
Step-by-step explanation:on kan
Can someone please give me the answer
Answer:
6/10
Step-by-step explanation:
30/50=3/5
3/5=3/5
15/25=3/5
3/5*2/2=6/10
TRUE OR FALSE , When you divide the numerator of a fraction by the denominator you always get a terminating decimal?
Answer: false.
Step-by-step explanation:
it's only a terminating decimal if you end up with a remainder of 0.
A recipe for a batch of muffins calls for 13 cup of sugar, 34 cup of flour, and 12 cup of milk. How many total cups of sugar, flour, and milk will be needed for three batches of muffins?
Answer:
177 total cups
Step-by-step explanation:
13×3=39 sugar
34×3=102 flour
12×3=63 milk
total 177
can someone give me the answer and please explain this to me because i really don't understand what this means at all, I need someone to help me with this because i'm going to be asking multiple of these questions. So if u have friends or family who know this answer then please tell/ask them these questions so they can help understand fractions. Not asking in a mean way i am just really cuious because i never learned how to do this so just let your family / or friends know what these answers are to all of the questions that i am going to ask about fractions because these are really hard for me!
Step-by-step explanation:
the one is the middle top the one in the middle bottom and the one in the bottom right
How to subtract? how can we minus 7 from 2 how can we maintain sign
Answer:
a² - b² = (a+b)(a-b)
Step-by-step explanation:
= 2x² - 7x²
=(2x + 7x)(2x - 7x)
Answer:
-5x²
Step-by-step explanation:
combine like terms in 2x²-7x²
Which number makes this number sentence true?
q: 7.05<____<7.2
o:A:7.016
B:7.182
C:7.206
D:7.241
Answer:
A: 7.016
Step-by-step explanation:
this is the answer. I'm 100% sure.
If Jada runs 5 laps around the track in 6 minutes how many minutes per lap is that
Answer:
1.2 minutes
Step-by-step explanation:
5 laps >> 360 ( 6×60)
1 lap >> x
cross multiplication
5x = 360
x = 360/5
x= 72 second
x = 72/60 = 1.2 minute
Your current salary is $32,000 per
year. If you get a 4% raise, how
much will you make now per year?
Answer:
$128,000 per yearStep-by-step explanation:
32,000
×. 4
Answer:
$33,280
Step-by-step explanation:
Since your salary is $32,000, you would take 4% from $32,000 and add it to the current salary. 4% can be shown as .04 in decimal form. If you multiply 32,000 by .04 you get 1280. Add 1,280 to 32,000 and you get 33,280.