the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
The binomial distribution, which models the number of successful trials (catches) in a certain number of independent trials (passes thrown), can be used to solve this problem.
The likelihood of not catching a pass is 0.2, but the likelihood of catching one is 0.8. The likelihood of catching at least 10 passes out of 15 can be calculated as follows:
P(X >= 10) equals P(X = 10) plus P(X = 11). + ... + P(X = 15)
where X is how many of the 15 passes were intercepted.
The probability of catching precisely k passes out of n can be calculated using the binomial distribution formula:
P(X = k) = (n choose k) × p²k × (1 - p)²(n-k)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.
Plugging in the values for n = 15, p = 0.8, and k = 10, 11, 12, 13, 14, and 15, we get:
P(X >= 10) = P(X = 10) + P(X = 11) + ... + P(X = 15)
= (15 choose 10) × 0.8²10 × 0.2²5 + (15 choose 11) × 0.8²11 × 0.2²4 + ... + (15 choose 15) × 0.8²15 × 0.2²0
≈ 0.987
Therefore, the probability that Juan will catch at least 10 passes out of 15 is approximately 0.987.
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A recent survey reported that 87% of Americans approve of human embryonic stem cell research. If an American is selected at random, find the probability that he or she will disapprove or have no opinion on the issue. The probability that he or she will disapprove or have no opinion on the issue is %?
The probability that an American will disapprove or have no opinion on the issue is 13%.
What is Probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used to describe random phenomena, such as the roll of a dice, the flip of a coin, the occurrence of an earthquake, or the outcome of a hand of poker. It is also used to describe the likelihood of certain events happening based on past data or current conditions.
This can be calculated by subtracting the reported approval rate of 87% from 100%. This means that 13% of Americans disapprove or have no opinion on the issue of human embryonic stem cell research.
It is important to note that this survey's data only pertains to the opinions of Americans and not to any other group of people. Therefore, the probability that any individual randomly selected from the global population will disapprove or have no opinion on the issue may be different.
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Prepare a statement of cash flows for Business Solutions using the indirect method for the three months ended March 31, 2022. Owner Santana Rey contributed $25,000 to the business in exchange for additional stock in the first quarter of 2022 and has received $4,800 in cash dividends.
The lateral area of a cone is 473pi cm^2. The radius is 43 cm. Find the height to the nearest tenth
The slant height of the cone is about 11 cm. Using the Pythagorean theorem, the height is approximately 41.4 cm to the nearest tenth.
Use the formula for the lateral area of a cone: L = πrs, where L is the lateral area, r is the radius of the base, and s is the slant height.
Plug in the given values: L = 473π cm² and r = 43 cm. Then solve for s
L = πrs
473π = π(43)s
s = 473/43 ≈ 11
So the slant height of the cone is approximately 11 cm.
Use the Pythagorean theorem to find the height of the cone. Let h be the height of the cone. Then the Pythagorean theorem gives
h² + s² = r²
Substituting in the values for s and r, we get
h² + 11² = 43²
Simplifying this equation, we get
h² = 43² - 11²
Evaluating the right-hand side, we get
h² = 1764
Taking the square root of both sides, we get
h ≈ 41.4
So the height of the cone is approximately 41.4 cm to the nearest tenth.
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Cruz has 64 stamps, of which 1/8 of the stamps have bees on them, and 3/16 of the stamps have flowers. The rest of the stamps have butterflies. How many stamps have butterflies on them? Explain.
Answer:
44 butterfly stamps
Step-by-step explanation:
1/8=2/16
2/16+3/16=5/16
16/16-5/16=11/16
64÷16=4
4×11=44
44/64
According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded.
(a) Find the probability that exactly 40 of the murders were cleared.
(b) Find the probability that between 35 and 37 of the murders, inclusive, were cleared.
(c) Would it be unusual if fewer than 20 of the murders were cleared? Why or why not?
The probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
(a) The probability that exactly 40 of the murders were cleared can be found using the binomial probability formula.
In this case, n = 50, k = 40, and p = 0.65. Thus, the probability that exactly 40 of the 50 murders were cleared is P(40 successes) = (50C40)(0.65)⁴⁰(0.35)¹⁰ = 0.064.
(b) The probability that between 35 and 37 of the murders, inclusive, were cleared can be found by adding the probabilities of each individual outcome.
For example, the probability of exactly 35 successes is (50C35)(0.65)³⁵(0.35)¹⁵ = 0.069.
Similarly, the probability of exactly 36 successes is (50C36)(0.65)³⁶(0.35)¹⁴ = 0.051.
Adding these two probabilities together gives the probability of between 35 and 37 successes, inclusive, as 0.069 + 0.051 = 0.120.
(c) It would not be unusual if fewer than 20 of the murders were cleared. This is because the probability of this outcome can be calculated using the same formula as before. In this case, if k = 19, then P(19 successes) = (50C19)(0.65)¹⁹(0.35)³¹ = 0.057, which is a relatively high probability.
Therefore, the probability that between 35 and 37 of the murders, inclusive, were cleared is 0.12.
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Kenji walks 44 feet in 10 seconds. At this rate, how many miles does Kenji walk in an hour? Show your work. (1 mile= 5,280 feet)
Answer:
44 feet in 10 seconds = 44 x 6 (since there are 60 seconds in a minute) = 264 feet per minute
264 feet per minute x 60 minutes (since there are 60 minutes in one hour) = 15,840 feet per hour
15,840 feet per hour / 5,280 feet (since there are 5,280 feet in 1 mile) = 3 miles per hour
T
2
√
k
aº
90°
Special Right Triangles
2
If the diagonal of a square produces an isosceles right
triangle, then you should be able to find the measures
of the base angles.
What is the measure of angles a and b?
angle
a
b
measure
check
X
X
The base angles a and b have their measures to be 45 degrees each
Calculating the base angles a and b?If the diagonal of a square produces an isosceles right triangle, then the two legs of the right triangle are congruent, meaning the two base angles are congruent as well.
Since the triangle is a right triangle, one of the base angles must be 45 degrees (which is half of the right angle).
Therefore, both base angles are 45 degrees.
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Help asap quickly math homework
Since line segment SP is a diameter, the measure of arc PTS is 180 degrees. 180 - 42 = 138 degrees, which is the measure of arc PT. 97 + 42 + 138 = 277 degrees for the measure of arc PTR
Determine the equation of straight line passing through the point (1,0) and (2, - 3)
first you need to find the gradient of the line and to do that you divide the height of a part of the line by its length. so to find the height we do -3-0=-3 and to find the length we do 2-1=1. then divide -3 by 1 and the gradient is -3. so now we know the equation is y=-3x+b. to find b we replace y with the y coordinate of one of the 2 points. lets take the first point. so it will be 0=-3+b. Now we can easily find b by doing 0-(-3) which is 3. so the equation of the line is y=-3x+3. Also please mark this as brainliest answer if you found it helpful thanks.
Answer:
y = - 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 0 ) and (x₂, y₂ ) = (2, - 3 )
m = [tex]\frac{-3-0}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (2, - 3 )
- 3 = - 3(2) + c = - 6 + c ( add 6 to both sides )
3 = c
y = - 3x + 3 ← equation of line
You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?
According to the concept of compound interest, the effective annual yield on your investment of $1800 at a 6.3% interest rate compounded daily is 6.49%.
To find the effective annual yield, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
Where A is the amount of money at the end of the investment period, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
In this case, we know that the principal amount P is $1800, the annual interest rate r is 6.3%, and the interest is compounded daily, which means that n is 365 (the number of days in a year). We need to find the effective annual yield, which is the total amount of interest earned in one year.
To calculate the effective annual yield, we can use the following formula:
Effective Annual Yield = (1 + r/n)ⁿ - 1
Plugging in the values, we get:
Effective Annual Yield = (1 + 0.063/365)³⁶⁵ - 1
Effective Annual Yield = 0.0649 or 6.49%
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factor each completely
6r2 + 31r + 18
Therefore, the expression 6r² + 31r + 18 factors completely into (3r + 2)(2r + 9).
What is factor?In mathematics, factoring is the process of finding the factors or divisors of a given number or algebraic expression. When we factor a number or expression, we find the numbers or expressions that can be multiplied together to obtain the original number or expression. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, since these numbers can be multiplied together in different combinations to obtain 12. Factoring is an important skill in algebra, as it helps us to simplify algebraic expressions and solve equations.
Here,
To factor the quadratic expression completely, we need to find two binomials whose product is equal to the given expression. We can start by looking for two numbers whose product is 6 x 18 = 108 and whose sum is 31. After some trial and error, we find that the numbers are 6 and 18.
We can now write the expression as:
=6r² + 31r + 18
18*6=108
27*4=108
27+4=31
= 6r² + 27r + 4r + 18
= 3r(2r + 9) + 2(2r + 9)
= (3r + 2)(2r + 9)
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What is the most descriptive name for the illustration below?
A. quadrilateral
B. polygon
C. rhombus
D. trapezoid
The most descriptive name for the illustration below is C. rhombus.
Define term Rhombus?Because it has four sides, a rhombus is a geometric shape that is a quadrilateral. Because its opposite sides are parallel and their angles are equal, it is a unique kind of parallelogram.
The most descriptive name for the illustration above is C. rhombus.
A rhombus is a type of quadrilateral with four sides of equal length and opposite angles that are equal to each other. It can also be defined as a parallelogram with equal diagonals. The illustration appears to have all sides of equal length and opposite angles that are equal, thus making it a rhombus.
While the other options, such as quadrilateral, polygon, and trapezoid, also apply to the illustration, they are less specific than the term rhombus.
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Allen plans to weld peices of metal together to create a metal cube the length of of each side of the cube will be 14 inches how much metal will he need to create the cube
Mathematics
Calculate the percentage, show your solution.
90% of 60
help, thanks!
Answer:
Your answer is 90% of 60 = 54.
Need help with his page 50 points
Answer: B, C, B
Step-by-step explanation:
see images for explanation
Answer:
[tex]\textsf{11)} \quad \text{b.}\;\;2\frac{3}{4}[/tex]
[tex]\textsf{12)} \quad \text{c.}\;\;7\frac{1}{2}[/tex]
[tex]\textsf{13)} \quad \text{b.}\;\;\dfrac{2}{3}x+4=10[/tex]
Step-by-step explanation:
Question 11To find the answer to the given equation when y = 4, substitute y = 4 into the equation:
[tex]\begin{aligned} y=4 \implies \dfrac{3}{4}+\dfrac{2(4)}{4}&= \dfrac{3}{4}+\dfrac{8}{4}\\\\&= \dfrac{3}{4}+2\\\\&= 2\frac{3}{4}\end{aligned}[/tex]
Therefore, the answer is 2³/₄.
[tex]\hrulefill[/tex]
Question 12To find the answer to the given equation when y = 8, substitute y = 8 into the equation:
[tex]\begin{aligned}y=8 \implies \dfrac{12}{8}+\dfrac{3(8)}{4}&= \dfrac{12}{8}+\dfrac{24}{4}\\\\&= \dfrac{12}{8}+6\\\\&= \dfrac{8+4}{8}+6\\\\&= \dfrac{8}{8}+\dfrac{4}{8}+6\\\\&= 1+\dfrac{1}{2}+6\\\\&=7\frac{1}{2}\end{aligned}[/tex]
Therefore, the answer is 7¹/₂.
[tex]\hrulefill[/tex]
Question 13To determine which equation is true if x = 9, substitute x = 9 into each equation.
[tex]\begin{aligned} \text{a)} \quad \dfrac{2}{3}(9)-6&=12\\\\\dfrac{18}{3}-6&=12\\\\6-6&=12\\\\0&=12\end{aligned}[/tex]
[tex]\begin{aligned} \text{b)} \quad \dfrac{2}{3}(9)+4&=10\\\\\dfrac{18}{3}+4&=10\\\\6+4&=10\\\\10&=10\end{aligned}[/tex]
[tex]\begin{aligned} \text{c)} \quad 3(9)-12&=21\\27-12&=21\\15&=21\end{aligned}[/tex]
[tex]\begin{aligned} \text{d)} \quad 3(9)+12&=19\\27+12&=19\\39&=19\end{aligned}[/tex]
Therefore, the only equation that holds true is option b.
Kleen Company acquired patent rights on January 10 of Year 1 for $881,100. The patent has a useful life equal to its legal life of eight years. On January 7 of Year 4, Kleen successfully defended the patent in a lawsuit at a cost of $49,200.
Required:
a. Determine the patent amortization expense for Year 4 ended December 31.
b. Journalize the adjusting entry on December 31 of Year 4 to recognize the amortization. Refer to the Chart of Accounts for exact wording of account titles.
whats the answer for log b + z log c in condense form
Answer:
log b.c^z
Step-by-step explanation:
from the theorem a log b=log b^a
z log c= log c^z
from the theorem log a + log b= log ab
log b+ log c^z= logb. c^z will be the final answer
I need help with this question. I cannot seem to get past it. Please help me
Answer:
dont know either
Step-by-step explanation:
dont know either
What is the length of side b? (Hint: There are 3 sides and 1 angle)
The length of side b is given as follows:
b = 2.86 m.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is obtained as follows:
B + 30 + 80 = 180
B = 70º.
Then the relation, by the law of sines, is given as follows:
sin(70º)/b = sin(80º)/3
Meaning that the length of side b is given as follows:
b = 3 x sine of 70 degrees/sine of 80 degrees
b = 2.86 m.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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The ratio of lime to sand in mortar is 3:7. How much lime must be mixed with 56 bags of sand to make mortar?
The ratio of the sand is 3:7 and it can be write as 6:14 or 7:21 ... They means the same thing.
Now we know that we have 56 bags of sand, the left side of the number should be 56. Like this:
? : 56
Since we know that 3:7 can be write as 6:14 or 7:21 ... we can even write it as 24:56, it's still 3:7.
ASAPP Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
C. d = 163t
Step-by-step explanation:
This equation represents a direct proportionality between the number of dollars earned (d) and the amount of time worked (t), with a constant of proportionality of 163 dollars per hour.
Hope this helps!
how do i solve this equation using factoring method?
x² - 14x + 9 = 0
Certainly!
The text is asking how to solve the equation x² - 14x + 9 = 0 using the factoring method. Factoring is a method of finding the roots of a quadratic equation by expressing it as a product of two linear factors. The roots of a quadratic equation are the values of x that make the equation equal to zero. In this case, we are trying to find the values of x that satisfy the equation x² - 14x + 9 = 0.
Cut this figure into 3 congruent parts along the sides of the cells. Can you cut it into 4 congruent parts?
its a 4 by 4, minus one square
Yes, the shape can be cut into 3 congruent parts but not 4. This is a whole number division problem. See the attached shape for how to divide the figure into 3 congruent parts.
What is Whole number division?In mathematics, when two numbers are divided without remainders, it is known as integer division or whole number division.
This specific kind of calculation comes in handy when you desire to find out just the quotient or how many times one number divides into another, disregarding any leftover fraction.
For instance, if we utilize integer division to calculate what happens when ten is divided by two; we're left with five as our answer since two divides equally into ten precisely five times without remaining any leftovers.
Conversely speaking though and in regards to regular arithmetic calculations; dividing ten by three amounts up to three with a remainder value attached since three cannot do so equally.
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Suppose you physically simulate the random process of rolling a single die. (a) After 1010 rolls of the die, you observe a "one" 44 times. What proportion of the rolls resulted in a "one"? (b) After 2020 rolls of the die, you observe a "one" 22 times. What proportion of the rolls resulted in a "one"?
Answer:
(a) 4.356% (b) 1.089%
Step-by-step explanation:
The rolling of a single die is an example of a discrete uniform distribution, where each of the six possible outcomes has an equal probability of 1/6.
(a) After 1010 rolls of the die, observing a "one" 44 times, the proportion of rolls resulting in a "one" is:
Proportion = Number of "ones" / Total number of rolls
= 44 / 1010
= 0.04356
Therefore, approximately 4.356% of the rolls resulted in a "one".
(b) After 2020 rolls of the die, observing a "one" 22 times, the proportion of rolls resulting in a "one" is:
Proportion = Number of "ones" / Total number of rolls
= 22 / 2020
= 0.01089
Therefore, approximately 1.089% of the rolls resulted in a "one".
Answer:
A) 40%
B) 10%
Step-by-step explanation:
A) p = 4/10 = 40%
B) p = 2/20 = 10%
Please help me! 20 points!!!
A rocket can travel at 8,000 meters per second. If d is the distance in meters and t is the time in seconds, what is the formula for how far the rocket travels in t seconds?
Enter your answer as a formula including "d(t)=".
The formula for how far the rocket travels in t seconds is d(t) = 8,000t.
What is speed?In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;
Miles per hour (mph).Kilometers per hour (kph).Meter per seconds (m/s).How to calculate the speed?In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Making distance the subject of formula, we have:
Distance, d(t) = speed × time
Distance, d(t) = 8,000 × t
Distance, d(t) = 8,000t
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From the set {1, 12, 17}, use substitution to determine which value of x makes the equation true. 36x + 31 = 535 A. 12 B. none of these C. 1 D. 17
ANWSER FAST!!!
The value of x in the equation is B) None of these.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation is 36x+31=535
Now substitute x=1 then,
=> 36(1)+31=535
=> 36+31=535
=> 67 ≠ 535
Now substitute x = 12 then
=> 36(12)+31=535
=> 432+31 = 535
=> 463 ≠ 535
Now substitute x= 17 then
=> 36(17)+31=535
=> 612+31 = 535
=> 643 ≠ 535.
Hence the correct option is B) None of these.
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Ruby is visiting San francisco. From her hotel she walks 4 block east and 3 blocks north to a coffee shop. Then she walks 7 blocks west and 1 blocks north to a museum. Where is the museum in relation to her hotel?
The museum in relation to her hotel is at distance and direction as 3 blocks to the west and 4 blocks to the north.
Given that,
Ruby is visiting San francisco.
The figure representing the situation is given below.
Here it is easier to find the relation of the museum with the hotel.
When Ruby walk a certain distance to the west, she will reach straightly north to the museum.
Distance to the west = 7 - 4 = 3 blocks
Then she can walk 3 + 1 = 4 blocks to reach the museum.
Hence the museum is at a distance of 3 blocks to the west and 4 blocks to the north.
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a city has a population of 280,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 12 years?
Step-by-step explanation:
Use a compounding formula like this:
P (t) = 280 000 (1 + .0725) ^t
t is years .0725 is 7.25% in decimal form
P (12) = 280 000 ( 1.0725)^12 = 648,523 population
Does each of these graphs have at least one Hamiltonian circuit? If so, find one.
The first shape does NOT have a Hamilton circuit
The second shape has a Hamilton circuit
The third shape does NOT have a Hamilton circuit
What is a Hamiltonian circuit?In mathematical graph theory, a Hamiltonian circuit- named after its originator William Rowan Hamilton, an acclaimed Irish mathematician of the 19th century– is a path within a graph that covers every vertex only once and begins and ends at the same vertex.
To put it differently, it's an enclosed movement that goes through each point in the graph exactly once. When the graph consists of a Hamiltonian circuit, this indicates to be a Hamiltonian graph. One can see many practical uses of Hamiltonian circuits such as computer science where they play a crucial role in algorithm analysis and design.
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The lengths of a particular animal's pregnancies are approximately normally distributed, with mean μ=257 days and standard deviation a = 8 days.
(a) What proportion of pregnancies lasts more than 267 days?
(b) What proportion of pregnancies lasts between 255 and 261 days?
(c) What is the probability that a randomly selected pregnancy lasts no more than 245 days?
(d) A "very preterm baby is one whose gestation period is less than 239 days. Are very preterm babies unusual?
a. It should be noted that about 10.56% of pregnancies last more than 267 days.
b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.
c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.
d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.
How to explain the probabilityIn this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:
z = (239 - 257) / 8 = -2.25
To the left of 239, there is:
P(X < 239) = P(Z < -2.25) = 0.0122
This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.
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a. It should be noted that about 10.56% of pregnancies last more than 267 days.
b. It should be noted that about 26.76% of pregnancies last between 255 and 261 days.
c. The probability that a randomly selected pregnancy lasts no more than 245 days is about 6.68%.
d. Only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event.
How to explain the probabilityIn this case, to see, to see if very preterm babies are uncommon, we must compare the likelihood of a pregnancy lasting less than 239 days to some criterion. We can employ the z-score:
z = (239 - 257) / 8 = -2.25
To the left of 239, there is:
P(X < 239) = P(Z < -2.25) = 0.0122
This suggests that only about 1.22% of pregnancies are extremely preterm, a somewhat uncommon event. As a result, very premature newborns are considered rare.
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