Answer:
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
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 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. Subtracting 1 by the p-value, 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.
Assume that the heights of men are normally distributed with a mean of "71.3" inches and a standard deviation of 2.1 inches.
This means that [tex]\mu = 71.3, \sigma = 2.1[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{2.1}{\sqrt{36}} = 0.35[/tex]
Find the probability that they have a mean height greater than 72.3 inches.
This is 1 subtracted by the pvalue of Z when X = 72.3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{72.3 - 71.3}{0.35}[/tex]
[tex]Z = 2.86[/tex]
[tex]Z = 2.86[/tex] has a pvalue of 0.9979
1 - 0.9979 = 0.0021
0.0021 = 0.21% probability that they have a mean height greater than 72.3 inches.
What is 442 divided by 13
Use the fundamental counting principle to determine all the possible outcomes from rolling a die once then spinning the spinner.
I just need the q1 med and q3
Answer:
Q1 = 6
Med = 12
Q2 = 15
Step-by-step explanation:
4764 to the nearest ten
Steven jogs around a circular field with a diameter of 70 yd. Find the area of the field.
Answer:
3848.46 :)
Step-by-step explanation:
An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck are defective after a year of use. It has contacted customers and asked them to return to their dealer after a year to have their transmission checked. The Friendly Auto Mart sold seven of these trucks and has two of the new transmissions in stock. What is the probability that they will need to order at least one more new transmission
Answer:
0.148 = 14.8% probability that they will need to order at least one more new transmission
Step-by-step explanation:
For each transmission, there are only two possible outcomes. Either it is defective after a year of use, or it is not. The probability of a transmission being defective is independent of any other transmission. This means that the binomial probability distribution is used 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.
20% of all the transmissions it installed in a particular style of truck are defective after a year of use.
This means that [tex]p = 0.2[/tex]
Sold seven trucks:
This means that [tex]n = 7[/tex]
It has two of the new transmissions in stock. What is the probability that they will need to order at least one more new transmission?
This is the probability that at least 3 are defective, that is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.2)^{0}.(0.8)^{7} = 0.2097[/tex]
[tex]P(X = 1) = C_{7,1}.(0.2)^{1}.(0.8)^{6} = 0.3670[/tex]
[tex]P(X = 2) = C_{7,2}.(0.2)^{2}.(0.8)^{5} = 0.2753[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2097 + 0.3670 + 0.2753 = 0.852[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.852 = 0.148[/tex]
0.148 = 14.8% probability that they will need to order at least one more new transmission
The population of Linton is 12 times as great
as the population of Ellmore.
The combined
population of both towns
is 9,646 people. What
the population of Linton
Answer:
8904 People
Step-by-step explanation:
We start by the equation L = 12E, where L represents the population of Linton and E represents the population of Ellmore. We then set L + E = 9646, but since L = 12E, we then get 12E + E = 9636, or 13E = 9646. Therefore, E = 742. L = 12E, so L = 8904.
Mackenzie thought that the basketball
team would win 16 games, but they
only won 12. What was his percent
error?
His percent error is 25% because 12 is 75% of 16. 100 - 75 = 25
Answer:
75% correct and 25%error
Step-by-step explanation:
As 12÷16×100=75%
The error =100-75=25%
9. Sally works in a cell phone store. She is paid a weekly salary of $80 plus $5.25 for each cel
phone she sells. Which equation can be used to find Sally's total weekly income?
Answer:
y = 5.25x + 80
Step-by-step explanation:
total income = 5.25 * phones + 80 salary
Answer:
y = 5.25x + 80
Step-by-step explanation:
The double number line shows the amount of time a hen needs to lay 1 egg.
Complete the table to show the same information as the double number line.
Eggs Time (hours)
3
100
12
I realize the double number line in this exercise can be as shown in the attached image, in that case, the table, correctly completed is:
Eggs Time (hours)
3 75
4 100
12 300
Method to complete the table.
First, you must see the double number line (attached image), in this we identify a hen needs 25 hours to lay 1 egg, by this reason, to identify the time required for a certain number of eggs, just multiply the number of eggs by 25 (the number of hours shown on the double number line), then:
3 * 25 = 7512 * 25 = 300To calculate the number of eggs taking into account the time, you must divide the hours by 25:
100 / 25 = 4In this way, you can check that the answers are 75, 4, and 300 respectively, to complete the table in the correct form.
You can review more exercises and test your new knowledge about the double number line at the following link: https://brainly.com/question/13553589?referrer=searchResults
Answer: eggs time
3 75
4 100
12 300
Step-by-step explanation:
Which statement best explains whether y = 2x − 3 is a linear function or a nonlinear function?
It is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
It is a nonlinear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are not on a straight line.
It is a linear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are on a straight line.
It is a nonlinear function because the graph contains the points (−3, 0), (−1, 1), (1, 2), which are not on a straight line.
Answer:
It is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
Step-by-step explanation:
(0,-3) goes on the straight line perfectly
(1, −1) goes on the straight line perfectly
(2, 1) goes on the straight line perfectly
this means that it is a linear function due to all the points being on the line
hope this helps!
The given function y = 2x − 3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
How to solve this problem?Given function y = 2x − 3.
Clearly, it is a straight line.
At x = 0, y = 2*0 - 3 = 0 - 3 = - 3
At x = 1, y = 2*1 - 3 = 2 - 3 = - 1
At x = 2, y = 2*2 - 3 = 4 - 3 = 1
So, the given straight line passes through the points (0, -3), (1, -1), and (2, 1). Then the given function is a linear function.
Therefore, we can conclude that the given function y = 2x − 3 is a linear function because the graph contains the points (0, −3), (1, −1), (2, 1), which are on a straight line. So, the first option is correct.
Learn more about linear functions here -
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I NEED YALL HELP PLEASE !!!! On 1,2,3
Answer:
1) 20%
2) 30%
3) 50%
Step-by-step explanation:
Answer:
1. 40%
2. 25%
3. 60%
Step-by-step explanation:
Please help ASAP this is due today
Answer:
good luck
Step-by-step explanation:
the mean is all of them added up then divided by how many numbers there are the median is where you put them in order putting the numbers in order then finding the middlel mode is the most of the same numbers and range is the biggest number
Answer:
mean- 104.83
median- 102
mode- 101
range- 28
Step-by-step explanation:
mean is all numbers added together then divided by however many numbers there are. sum of all numbers is 629, divided by 6 is 104.83 repeating.
median is the number in the middle. since there are six numbers and no middle one, the two in the middle (when ordered smallest to largest) are 101 and 103. the number between those two is 102 and therefore the median.
mode is the number that appears the most in the data set, which is 101 in this case.
range is the difference between the largest number and the smallest. the largest number is 121, minus 93, the smallest number, gives you 28.
hope this helps!
If g(x) = -3(x) - 5 then g(?) = 25
10
-20
5
-10
Answer:
D) -10
Step-by-step explanation:
We will assign g(x) to be equal to 25, and then solve for x:
25 = -3x-5
30 = -3x
10 = -x
-10 = x
So D is correct
Answer:
-10 is correct option
Step-by-step explanation:
g(x)=-3(x)-5
g(-10)=-3(-10)-5
=30-5
=25
Solve the polynomial equation = 3
Answer:
lol the is no equation there to solve
What is the probability of choosing a king of hearts or a queen of spades from a deck of cards? Type your answer as a fraction.
Answer:
Step-by-step explanation:
1 /13
Answer:
1/13???
Step-by-step explanation:
Help if you can :)
Also, show work!
Plz dont add any type of link
thxx <3
98 is what percent of 280?
Answer:
35%
Step-by-step explanation:
Find the percent by dividing 98 by 280
98/280
= 0.35
So, 98 is 35% of 280
A right angled triangle has a second angle equal 24 degrees. The side adjacent to this angle is 3,7 metres long. How long are the hypotenuse and opposite sides? (3)
HURRY Antoine is using a horse trailer to transport his horses to his new
ranch.
A. Complete the table by finding the weight, in pounds, of
Antoine's horse trailer and each horse.
+
Weight (T)
Weight (lb)
Horse
0.4
Trailer
1.5
SHIFT Draw circle
Answer:
Step-by-step explanation:
Any help? I need to describe the change of the equation, in terms of it getting thinner (>) or wider (<). I don't exactly understand how to do this, can anyone explain?
9514 1404 393
Answer:
no change to the width of the curve
Step-by-step explanation:
Your terminology and use of symbols (>, <) are unusual, so we're not sure what your question is.
The equation represents a transformation of the parent function
y = x²
The transformation (replacing x with (x-4)) is a translation right 4 units. This can be seen in the attached graph. The "parent function" is shown in red. Your function is shown in blue.
Nothing about this transformation changes the width of the curve, so it is neither thinner nor wider than it was originally. The description usually used if the curve is narrower or wider is "horizontal compression" or "horizontal expansion."
The curve does get wider for larger y-values. It is said to "open upward".
__
Additional comment
The symbols < and > stand for "is less than" and "is greater than", respectively. They are occasionally used as "angle brackets" to identify vectors or tokens of one sort or another. Sometimes, they are used to signify an angle when the appropriate ∠ symbol is not available. This is the first time in many years of studying math that I have seen them in the context of "thinner" and "wider."
This shape has all identical faces and a surface area of 240 square meters. What is the area of each face?
A 120
B 80
C 60
D 30
Help anyone? Math is not my strong suit
Answer:
the 3rd one
Step-by-step explanation:
Answer:
it's the 7 one
Step-by-step explanation:
math has patterns if you follow the patterns you can see the symbol and the 7 look alike. stuff like this works for me a lot but I don't know f it'll work this time. If it doesn't I'm sorry I tried.
What is the median of the numbers 63,5,0,0,45,2,23,16
Answer:
10.5
Step-by-step explanation:
63,5,0,0,45,2,23,16
order from smallest to greatest
0, 0, 2, 5, 16, 23, 45, 63
median = center number
(5 + 16) / 2 =10.5
what is the value of 9 in the number 2,093,507 please no links
Answer:
ten thousands
b bananas cost $1.45 and a apples cost $2.35.
(a) How much does one banana cost?
(b) How much does one apple cost?
(c) Write as a single fraction the cost of one
banana and one
apple.
The required one banana cost, one apple cost, and a single fraction $1.45/b, $1.45/b, and 0.54* a/b respectively.
In mathematics, it deals with numbers of operations according to the statements.
There is b number of bananas and a number of apples.
The cost of total bananas and apples is $1.45 and $2.35.
(a) Cost of one banana is,
For b bananas = $1.45
dividing both side by b
b/b bananas = $1.45/b
1 banana = $1.45/b
(b) Cost of one apple is,
For a apples = $2.35
dividing both side by a
a/a = $2.35/a
1 apple = $2.35/a
(c) Single fraction is given by = cost of one banana/ cost of one apple
= (1.25/b) / (2.35/a)
= 0.54* a/b
Thus the required one banana cost, one apple cost and single fraction $1.45/b, $1.45/b, and 0.54* a/b respectively.
Learn more about arithmetic here:
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In circle A measure of arc BD-56' and BC is a diameter. Which statements are correct?
Answer:
90 degrees and 80 degrees
12+98=
really confused on this one
Answer:
12+98=110
Step-by-step explanation:
FOR BRANLIEST PLEASE HELP!!
Answer:
75°
Step-by-step explanation:
<4=<105 because they are corresponding angles.
Angles along a straight line add to 180°, so <1+<4=180. Therefore <1=180-105=75°
10. What is the measure of ZP?*
E
(15m + 17)º
-Q
(4m – 10)
P
(7m - 9)
Answer:
m∡P = 40°
Step-by-step explanation:
15m + 17 + 4m - 10 + 7m - 9 = 180
26m - 2 = 180
26m = 182
m = 7
∡P = 7(7) - 9 = 49 - 9 = 40
