Answer: 140
Step-by-step explanation:
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The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 207.50 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30
Answer:
a) P(X > 207.50) = 0.0808
b) P(X-bar > 193.5) = 0.7734
c) It matters only in sampling distribution when we does not know the shape of distribution.
Step-by-step explanation:
Given - The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm.
To find - a. Find the probability that an individual distance is greater than 207.50 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ?
Proof -
Given that,
μ = 195 cm
σ = 8.9 cm
a)
P(X > 207.50) = 1 - P(X < 207.5)
= 1 - P(Z < [tex]\frac{207.5 - 195}{8.9}[/tex] )
= 1 - P(Z < 1.4)
= 1 - 0.9192
= 0.0808
⇒P(X > 207.50) = 0.0808
b)
n = 20
μₓ- = μ = 195
σₓ⁻ = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{8.9}{\sqrt{20} }[/tex] = 1.99
Now,
P(X-bar > 193.5) = 1 - P(X-bar < 193.5)
= 1 - P(Z < [tex]\frac{193.5 - 195}{1.99}[/tex] )
= 1 - P(Z < -0.75)
= 1 - 0.2266
= 0.7734
⇒P(X-bar > 193.5) = 0.7734
c)
Given that If the population is normally distributed , then the sample does not have to be greater than 30.
It matters only in sampling distribution when we does not know the shape of distribution.
Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/ h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).
Answer:
18 km/hStep-by-step explanation:
Let the speed of Baba Yaga is x
The speed with tailwind: x + 2The speed with headwind: x - 2The distance to Bald Mountain:
6(x + 2)The distance she actually travelled is less by 40 km:
6x + 12 - 40 = 6x - 28The time she spent:
(6x - 28)/(x+2) + (6x - 28)/(x -2) = 9Solve for x to find the speed:
((6x + 12) - 40)/(x + 2) + ((6x - 12) - 16)/(x - 2) = 96 - 40/(x + 2) + 6 - 16/(x - 2) = 940/(x + 2) + 16/(x - 2) = 340(x - 2) + 16(x + 2) = 3(x+2)(x - 2)40x - 80 + 16x + 32 = 3x² - 123x² - 56x + 36 = 0Solving the quadratic equation we get:
x = 18 km/h(x = 2/3 discounted as not realistic)What is the area of this square?
6xq=54 what is q? PLEASE HURRY THIS IS DUE TOMORROW!!!!!!!!!
how do you solve the inequality -8x is greater than 72
Answer:
8n < 72
Step-by-step explanation:
Eight times a number (n) is less than 72.
help mee pleaseeeeee
Answer:
Option 1
Step-by-step explanation:
Find the GCF of the numbers. 8, 16
Answer:
8
Step-by-step explanation:
Answer:
What is the Greatest Common Factor of 8 and 16? Greatest common factor (GCF) of 8 and 16 is 8.
hope it help plz heart and vote plz po..
The quotient of 6 and a
number (n)
Answer:
n divided by 6 (n/6)
Step-by-step explanation:
The mathematical expression for 'the quotient of 6 and a number (n)' is, 6/n or (6 ÷ n).
Used the concept of mathematical expression which can be stated that,
A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
The algebraic expression is,
''The quotient of 6 and a number (n).''
Now, the mathematical expression for 'the quotient of 6 and a
number (n)' is,
6 ÷ n
= 6 / n
So, the mathmatical notation is 6/n.
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The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is
Answer:
[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]
In which x is the number of which we want to find the probability.
Step-by-step explanation:
For each traffic fatality, there are only two possible outcomes. EIther it involved an intoxicated or alcohol-impaired driver or nonoccupant, or it didn't. Traffic fatalities are independent of other traffic fatalities, which means that the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant.
This means that [tex]p = 0.4[/tex]
Eight traffic fatalities
This means that [tex]n = 8[/tex]
Find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is
This is P(X = x), in which x is the number of which we want to find the probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]
Based on the binomial probability principle, the probability involving the number of non-occupant is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]
Let :
Number of alcohol - impaired or non-occupant = kNumber of trials, n = 8Probability of success, p = 0.40q = 1 - p = 1 - 0.40 = 0.60Using the binomial probability relation :
[tex] P(x = x) = nCx \times p^{x} \times q^{n-x} [/tex] x = kSubstituting the values into the relation :
[tex] P(x = k) = nCk \times 0.40^{k} \times 0.60^{n-k} [/tex]
Hence, the required probability expression is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]
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The true answer is 3.75
Answer:
interesting
Step-by-step explanation:
very interesting
Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?
y = 12x - 16
y = 12x + 16
y = 16x - 12
y = 16x + 12
Answer:
the first one
Step-by-step explanation:
y-y1=m(x-x1)
y-20=12(x-3)
[tex]y-20+20=12\left(x-3\right)+20[/tex]
simplify:
[tex]y=12x-16[/tex]
construct a triangle with is side ab 6.5 cm BC as 4cm and angle b as 120°
Answer
A triangle can be constructed if we are given 2 sides and an angle. For these ... AB=4 cm, Angle A =30˚, AC=5 cm. 2.) BC=3 cm, Angle B=80˚, BA=6 cm ... Angle A=20˚, AC=6.5 cm, Angle C=90˚ ... Angle A=25˚, Angle B=120˚, Angle C=35˚.
Step-by-step explanation:
⚠️PLEASE HELP⚠️
What is the value of the interquartile range of the data below?
25
30
35
40
45 50
Answer:
5
Step-by-step explanation:
The value of the interquartile range of the data below is 5.
What is Interquartile Range?The difference between the third and the first quartile is defined by the interquartile range. There are so three quartiles.
The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.
From the Plot we can write
Minimum = 27
Lower quartile = 32
Median = 36
Upper Quartile = 37
Maximum = 40
So, Interquartile range (IQR)
= Third Quartile (Q3) - First Quartile (Q1)
= 37 - 32
= 5
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Which function has the greater maximum value, f(x) or g(x)?
Answer:
g(x) is correct because if you look at the top of each parabola graph, you'll see how the vertex (the point in the middle top of the parabola) is higher than the other vertex of the function f(x). The y-coordinate of the vertex is the max/mini value, the x- coordinate of the vertex is the line of symmetry.
I applied this to my own problem and got it correct! You can use d e s m o s to see how the graph looks, and compare them. Good Luck!
Please and I’ll give Brain list to you
Answer:
e
Step-by-step explanation:
e
Answer:
6
Step-by-step explanation:
: What does the value of f(3) represent in the given context?
A.
After 4 bounces the height of the ball is 3 feet.
B.
After 4 bounces the height of the ball is 4 feet.
C.
After 3 bounces the height of the ball is 3 feet.
D.
After 3 bounces the height of the ball is 4 feet.
Answer: D
Step-by-step explanation: on The graph it shows the height of the ball after 3 bounces is 4 feet
Please answer quick just super small explanation pls hurry quick for brainlessly
Answer:
A = 81
Step-by-step explanation:
When there is a number above the other. You will need to multiply it.
There is a 4 so its 4 times.
-3 x -3 = 9
9 x -3 = -27
-27 x -3 = 81
------
When you multiply a negative number by a negative number it will be a positive.
If you multiply a positive number by a negative it will be negative.
What is the ratio as a fraction 9 and 6
Answer:
9/15 will become 3/5 and 6/15 will become 2/5.
Only answer if you know!!! Which expression represents 5 less than y? (1 point)
Oy-5
O 5-y
Oy
5
O5y-1
Answer:
5 less than y isn’t up there but if you mean 5 minus y it’s the second one, and y minus 5 is the first
Step-by-step explanation:
Which table or graph shows the value of y going down as the value of x goes
up?
Answer:
A
Step-by-step explanation:
That's your answer...
dang u fail gonna fail i feel baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad.......
just look at the one that has the letter x going up it is c or d
Solve the exponential equation.
2-x = 16
4
1/4
-4
Answer:
-4
Step-by-step explanation:
Find the area of the polygon.
Answer:
Step-by-step explanation:
A = (7 + 4)(24) ÷ 2 = 132 units²
is 32/24 equivalent to 12/9
Answer:
32/24 is equivalent to 12/19
yes
What is the correct answer I’m offering brainalist + 10 points don’t just say A please can you explain to me why you chose what you chose
Answer:
Answer is Complementary.
Step-by-step explanation:
This is because complementary angles add up to 90 degrees. In this example, the angles are exactly 45 degrees. Therefore, because there are two angles 45 * 2 is 90. Answer is B.
Answer:
D. vertical
Step-by-step explanation:
We can rule out A and B because they wont equal 180 or 90 they will be somewhere in between. We can rule out C because those are acute angles. So we are left with D. These angles are vertical because they are opposite angles made by two intersecting lines and they have equal values.
PLEASE HELP mathematics
Answer:
21+10.5 which would equal 31.5
Step-by-step explanation:
Answer:
21+10.5 which would equal 31.5
Step-by-step explanation:
PLEASE PLEASE PLEASE!
Answer:
70
Step-by-step explanation:
The area of one of the four triangles is [tex]\frac{1}{2}\times 5 \times 7 = 17.5[/tex]. So together the area of all the four traingles is [tex]4\times 17.5 = 70[/tex]
PLS PLS PLS HELP ME
Answer:
A) x > -5
Step-by-step explanation:
Ms. Perry spent $2000 to buy some new computer equipment. Of this money, $120 was used to
buy some new keyboards. What percent of the money was spent on keyboards?
Answer: 6%
Step-by-step explanation: Step 1: We make the assumption that 2000 is 100% since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: From step 1, it follows that 100%=2000$.
Step 4: In the same vein, x%=120.
Step 5: This gives us a pair of simple equations:
100%=2000(1).
x%=120(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
[tex]\frac{100\%}{x\%}=\frac{2000}{120}[/tex]
Step 7: Taking the inverse (or reciprocal) of both sides yields
[tex]\frac{x\%}{100\%}=\frac{120}{2000}[/tex]
[tex]\Rightarrow x=6\%[/tex]
Therefore, 120 is 6% of 2000$.
if you saw one of your best friends getting bullied what would you do would you A help him/she B Just walk away C ask someone else for help D laugh at him cause I would help
Answer:
A. help him/her
funny story, i once got into trouble for defending my friend from being bullied and the person doing the bullying didn't get punished smh
Answer:
a
Step-by-step explanation:
duhh
Find the measure of 43.
92 88°
43
88
43 = [?]
please help I will give you brainlist just no links
Answer:
88°
Step-by-step explanation:
Because, vertically opposite angles are equal