Answer:
a
[tex]P(\= X \ge 51 ) =0.0062[/tex]
b
[tex]P(\= X \ge 51 ) = 0[/tex]
Step-by-step explanation:
From the question we are told that
The mean value is [tex]\mu = 50[/tex]
The standard deviation is [tex]\sigma = 1.2[/tex]
Considering question a
The sample size is n = 9
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_x = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_x = \frac{ 1.2 }{\sqrt{9} }[/tex]
=> [tex]\sigma_x = 0.4[/tex]
Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as
[tex]P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_{x}} \ge \frac{51 - 50 }{0.4 } )[/tex]
[tex]\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )[/tex]
[tex]P(\= X \ge 51 ) = P( Z \ge 2.5 )[/tex]
=> [tex]P(\= X \ge 51 ) =1- P( Z < 2.5 )[/tex]
From the z table the area under the normal curve to the left corresponding to 2.5 is
[tex]P( Z < 2.5 ) = 0.99379[/tex]
=> [tex]P(\= X \ge 51 ) =1-0.99379[/tex]
=> [tex]P(\= X \ge 51 ) =0.0062[/tex]
Considering question b
The sample size is n = 40
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_x = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_x = \frac{ 1.2 }{\sqrt{40} }[/tex]
=> [tex]\sigma_x = 0.1897[/tex]
Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as
[tex]P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_x} \ge \frac{51 - 50 }{0.1897 } )[/tex]
=> [tex]P(\= X \ge 51 ) = P(Z \ge 5.2715 )[/tex]
=> [tex]P(\= X \ge 51 ) = 1- P(Z < 5.2715 )[/tex]
From the z table the area under the normal curve to the left corresponding to 5.2715 and
=> [tex]P(Z < 5.2715 ) = 1[/tex]
So
[tex]P(\= X \ge 51 ) = 1- 1[/tex]
=> [tex]P(\= X \ge 51 ) = 0[/tex]
Using the normal distribution and the central limit theorem, we have that there is a:
a) 0.0062 = 0.62% probability that the sample mean hardness for a random sample of 9 pins is at least 51.
b) 0% approximate probability that the sample mean hardness for a random sample of 40 pins is at least 51.
In a normal distribution with mean and standard deviation , 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. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 50, hence [tex]\mu = 50[/tex]Standard deviation of 1.2, hence [tex]\sigma = 1.2[/tex]Sample of 9, hence [tex]n = 9, s = \frac{1.2}{\sqrt{9}} = 0.4[/tex].Item a:
The probability is 1 subtracted by the p-value of Z when X = 51, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.4}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
1 - 0.9938 = 0.0062
There is a 0.0062 = 0.62% probability that the sample mean hardness for a random sample of 9 pins is at least 51.
Item b:
Even though the distribution is not normal, the sample size is of [tex]n = 40 > 30[/tex], hence the Central Limit Theorem can be applied.
[tex]s = \frac{1.2}{\sqrt{40}} = 0.19[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{51 - 50}{0.19}[/tex]
[tex]Z = 5.26[/tex]
[tex]Z = 5.26[/tex] has a p-value of 1.
1 - 1 = 0
0% approximate probability that the sample mean hardness for a random sample of 40 pins is at least 51.
A similar problem is given at https://brainly.com/question/24663213
how many 2/3 size pieces are in 4 wholes
Answer:
3rd
Step-by-step explanation:
the 3rd makes 1 whole
what number should be added to 1253 to get 3000
Answer:
1747
Step-by-step explanation:
3000 - 1253 = 1747
Therefore 1747 should be added to 1253 to get 3000.
please hurry need help now
What is the solution to Ex- 3? 25 Ox> 18 25 Ox>2 O x
Answer: c, but I’m not totally sure
Step-by-step explanation:
The amount of gasoline G sold each month to customers at Bob's Exxon station in downtown Navasota is a random variable. This random variable G can be described as having a normal distribution with mean 2500 gallons and a standard deviation of 250 gallons (and there is no seasonal variation in sales). Exxon will give Bob an all-expense paid trip to College Station, including a free dinner at Burger King, if his station pumps more than 3000 gallons in any one month.
Required:
What is the probability that Bob will win that wonderful trip on the basis of his gasoline sales this month?
Answer:
The probability is [tex]0.0228[/tex]
Step-by-step explanation:
Let's start by defining the random variable [tex]G[/tex] as :
[tex]G:[/tex] '' The amount of gasoline sold each month to customers at Bob's Exxon station in downtown Navasota ''
Therefore, if [tex]X[/tex] is a continuous random variable that has a normal distribution, we write [tex]X[/tex] ~ [tex]N[/tex] ( μ , σ )
Where ''μ'' is the mean and ''σ'' is the standard deviation.
For the random variable [tex]G[/tex] we write :
[tex]G[/tex] ~ [tex]N(2500,250)[/tex]
We need to find [tex]P(G>3000)[/tex]
In order to calculate this, we are going to standardize the variable. This means, finding the equivalent probability in a normal random variable
[tex]Z[/tex] ~ [tex]N(0,1)[/tex]
We perform this because the random variable [tex]Z[/tex] ~ [tex]N(0,1)[/tex] is tabulated in any book or either you can find the table on Internet.
To standardize the variable we need to subtract the mean and then divide by the standard deviation ⇒
[tex]P(G>3000)[/tex] ⇒ P[ (G - μ) / σ > [tex]\frac{3000-2500}{250}[/tex] ] ⇒ [tex]P(Z>2)[/tex]
Because (G - μ) / σ ~ [tex]Z[/tex]
Finally, [tex]P(G>3000)=P(Z>2)[/tex] ⇒ [tex]P(Z>2)=1-P(Z\leq 2)[/tex] = 1 - Φ(2)
Where '' Ф(x) = [tex]P(X\leq x)[/tex] '' represents the cumulative function of [tex]Z[/tex]
Looking for Φ(2) in any table,
[tex]P(G>3000)=P(Z>2)=1-P(Z\leq 2)=1-0.9772=0.0228[/tex] ≅ %2.28
We found out that the probability is [tex]0.0228[/tex]
What is the slope of the line going through the points (2,5) and (-4,-1)?
Answer: The answer is 1.
Step-by-step explanation: The entered points belong to an increasing, linear function.
Equation: y = 1x + 3.
A company weighs 1,096 boxes of cereal and finds that 12.5% of them weighed less than one pound. Which of
the following is the number of boxes that weighed less than one pound?
Answer:
500
Step-by-step explanation:
HELP ASAP! What are the slope and y-intercept of the linear function that is represented by the table?
A. The slope ls -2, and the y-intercept is 6.
B. The slope ls -2, and the y-intercept is 12.
C. The slope is 2, and the y-intercept is 6.
D. The slope is 2, and the y-intercept is 12.
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
Use two points and find slope initially so,
(-3,18) (0,12)
18-12=6 , -3-0= -3
so the slope is 6/-3 = -2 so by this answer is either a or b .
further apply y =mx + c as it linear to find c
y= -2x + c
0 = -2x6 + c
c = 12
so slope is -2 , c is 12
Raise to the power:
c
(–3y)4
Answer:
3^4 x y^4
Step-by-step explanation:
Helopppppp pleaseeeeeee
Answer:
x=2, x=1/2, x=-2/3
Step-by-step explanation:
First factor and get (x-2)(2x-1)(3x+2)=0
Then you set each of these parentheses individually equal to 0. x-2=0, 2x-1=0, 3x+2=0. Then you just simplify these to get your final answer that I showed above.
90 people attended the movies yesterday. 87 people attended the movies today. Is this an increase or decrease? What was the percent change?
Answer:
This is a decrease
Step-by-step explanation:
3.33%
$3.29 for 9.25 ounces
How much is it per ounce?
Answer:
About $0.36 per ounce
Step-by-step explanation:
Set up a proportion.
Let p = price per ounce
3.29/p = 9.25 ounces/(1 ounce)
9.25p = 3.29
p = 3.29 ÷ 9.25
p = 0.3556756757
We can say 35 cents per ounce or 36 cents per ounce if rounded to 2 decimal places.
One number is three less than another number. If their sum is 49, find the two numbers.
Answer:
21 and 28
Step-by-step explanation:
Suppose you scored 95 on a measure where the mean was 110 and the standard deviation was 15. Assuming a normal distribution, what percentage of scores should fall between your score and the mean?
Answer:
34% of scores should fall between your score and the mean.
Step-by-step explanation:
Let X denote the score.
It is provided that X follows a normal distribution with mean 110 and standard deviation 15.
A students score, x = 95.
Compute the probability of scores that should fall between the student's score and the mean as follows:
[tex]P(95<X<110)=P(\frac{95-110}{15}<\frac{X-\mu}{\sigma}<\frac{110-110}{15})[/tex]
[tex]=P(-1<Z<0)\\\\=P(Z<0)-P(Z<-1)\\\\=0.50-0.15866\\\\=0.34134\\\\\approx 0.34[/tex]
Thus, 34% of scores should fall between your score and the mean.
Shana, who lives in Canada, and Pearl, who lives in Pennsylvania, were discussing the weather. Shana complained about the cold temperature of Negative 20 degrees Celsius. Pearl, who lives in Pennsylvania, mentioned that her temperature was the opposite of Shana’s. Which is the correct way to represent “the opposite of Shana’s temperature is equal to Pearl’s”? Negative 20 = 20 Negative (negative 20) = negative 20 Negative (20) = negative 20 Negative (negative 20) = 20
Answer:
the answer is -20 =20
Step-by-step explanation:
the opposite of 20 is -20
Answer:
im going to edit it when i finish the quiz
Step-by-step explanation:
Ok this is the edit and the person above me is wrong so i think it would be - ( -20) = 20 or D
mickey is typing in the computer lab and typing at 23 words per minute if he types for 11 minutes how many words does he type
Answer:
253 wpm
Step-by-step explanation:
23*11 which is 253.
Hope this helps plz mark brainliest :D
Find the value of 5a2−2a−10 if a=−6
ANSWER FOR BRAINLIEST
Hi there!
[tex]\large\boxed{182}[/tex]
Equation:
5a² - 2a - 10 for a = -6.
Evaluate by plugging in -6 for a:
5(-6)² - 2(-6) - 10 =
5(36) - (-12) - 10 =
180 + 12 - 10 = 182.
Select the correct answer.
It is 170 miles from Bruce's house to the city where his brother lives. On his last trip to visit his brother, he drove for 2 hours at 55 miles per
hour. Then he came to some very bad road construction. The rest of the trip took 2 hours. How many miles per hour did Bruce drive for the rest
of the trip?
Va
Answer:
He drove the rest of the trip at 30 miles per hour
Step-by-step explanation:
The rule of the distance is D = v × t, where
v is the speedt is the time∵ It is 170 miles from Bruce's house to the city where his brother lives
∴ D = 170 miles
∵ He drove for 2 hours at 55 miles per hour
∴ t1 = 2 hours and v1 = 55 miles/hour
→ By using the rule above find the distance of this part of his trip
∴ D1 = 55 × 2 = 110 miles
∵ The rest of the trip took 2 hours
∴ t2 = 2 hours
∵ D = D1 + D2
→ Substitute the values of D and D1 to find D2
∴ 170 = 110 + D2
→ Subtract 110 from both sides to find D2
∴ 60 = D2
∴ D2 = 170 - 110 = 60 miles
∵ The rest of the trip is 60 miles
∵ It took 2 hours
∵ D2 = v2 × t2
∴ 60 = v2 × 2
→ Divide both sides by 2
∴ 30 = v2
∴ v2 = 30 miles/hour
∴ He drove the rest of the trip at 30 miles per hour
Click on the picture do number 18 and 19
Answer:
<1=<2Being vertical angles
<2+<3=90° Being complementary angle
m<3=56
now
<2+<3=90
<2=90-56
<2=34
:.<1=34°
a) ¿Cuántas décadas han transcurrido desde 1917 hasta 2020
Round these numbers to the hundred- 6,232 490- 23,058
Answer:
6,200 500 23,000
Hoped this helped:)
Step-by-step explanation:
Answer:
6,232 rounded is 6,200
490 rounded is 500
23,058 rounded is 23,100
6 and 5 hundredths written in decimal
Answer:6.05
Step-by-step explanation:
6 is the ones place. 0 is the tenths place. 5 is the hundredths place.
what is the length of BC
Answer:
17
Step-by-step explanation:
this is an isosceles triangle so AB = AC
2x-8 = x + 9
x -8 = 9
x = 17
so CB = 17
Hi can you please tell me the answe to this question its due in a few mins. Thank you so much!!
Answer:
LNO I BELIEVE
Step-by-step explanation:
IT MAKES THE SAME SHAPE THAT NMO MAKES
Can someone help me solve this
Answer:
sin x = -5/13
csc x = -13/5
sec x = 13/12
cot x = -12/5
tan x = -5/12
Step-by-step explanation:
**x is in quadrant iv because 3pi/2<x<2pi
if cos x=12/13, then 12 is the adjacent value and 13 is the hypotenuse value. to find sin, or opposite/hypotenuse, use the pythagorean identity. opposite=5 and hypotenuse is given as 13. & since it's in quad iv, the sine (or y) value is negative bc it's below the x axis. thus, sin x = -5/13csc is cosecant, or the reciprocal of sine. so csc x = -13/5sec is secant, or the reciprocal of cosine. so sec x = 13/12tan is opp/adj, so tan x = -5/12. it's negative bc tan is negative in quad ivcot is cotangent, or the reciprocal of tangent. so cot x = -12/5Answer:
8. sin x = -5/13
9. csc x = -13/5
10. sec x = 13/12
11. cot x = -12/5
12. tan x = -5/12
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you with the sine and tangent. You need to rely on your memory (or notes) to find the reciprocal functions.
The dimensions are such that you can recognize this as a 5-12-13 right triangle. Or, you can use the Pythagorean theorem to find the third side from ... O = -√(H² -A²) = -√(169 -144) = -√25 = -5
The given quadrant tells you that O is negative.
__
8. Sin = Opposite/Hypotenuse
Here, the opposite is -5. The hypotenuse is always taken to be positive.
sin x = -5/13
__
9. Csc = 1/Sin
csc x = -13/5
__
10. Sec = 1/Cos
sec x = 13/12
__
11. Cot = 1/Tan = Adjacent/Opposite
cot x = 12/-5
cot x = -12/5
__
12. Tan = Opposite/Adjacent
tan x = -5/12
Kevin has four apples in a boat each apple weighs 60 G and the empty bowl weighs 40 grams what is the total weight of the four apples with the bow
9514 1404 393
Answer:
280 g
Step-by-step explanation:
The total weight is the sum of the weights of the objects:
total = bowl + apple + apple + apple + apple
We use multiplication to simplify repeated sums:
total = bowl + 4 × apple
total = (40 g) + 4 × (60 g) = 40g + 240 g
total = 280 g
The bowl and 4 apples weighs 280 grams.
A vector has a horizontal component of 14 and a vertical component of 36. Find the direction angle and the magnitude. Direction angle?
Answer:
The direction angle is 68.73 degrees and its magnitude is 38.62.
Step-by-step explanation:
Given that,
The horizontal component of a vector = 14
The vertical component of a vector = 36
Let the magnitude of a vector is v. So,
[tex]v=\sqrt{14^2+36^2} \\\\=38.62[/tex]
For direction,
[tex]\tena\theta=\dfrac{y}{x}\\\\=\dfrac{36}{14}\\\\\theta=\tan^{-1}(2.57)\\\\=68.73^{\circ}[/tex]
So, the direction angle is 68.73 degrees and its magnitude is 38.62.
What’s the product of (23-8c) - (5c-1)
Answer:
[tex]40c^{2}[/tex] -123c + 23
Step-by-step explanation:
1. First you need to distribute the negative sign to the second binomial
(23 - 8c) - (5c - 1)
(23 - 8c) (-5c + 1)
2. Distribute each term in the first binomial to each term in the second binomial, FOIL (first, outer, inner, last)
(23 - 8c) (-5c + 1)
-115c + 23 + [tex]40c^{2}[/tex] -8c
3. Combine the like terms
-115c + 23 + [tex]40c^{2}[/tex] -8c
[tex]40c^{2}[/tex] -123c + 23
hope this helps!
What is the slope of this line? Plz
Answer:
-2
Step-by-step explanation:
Suzy wants a triangular sandbox. Her dad makes a sandbox/triangle out of boards that are 9 ft, 12 ft, and
15 ft. Does Suzy's sandbox make a right triangle?
O True
O False
Susan has a piggy bank with 28 coins in it, all dimes and quarters. She has been collecting state quarters and so far has no repeats. If the piggy bank has $5.50. how many more quarters does Susan need before she has a quarter from each of the 50 states?
HELP I WILL GIVE POINTS AND BRAINLIEST
Answer:
She needs 32 quarters.
Step-by-step explanation:
d = dime q = quarters
d + q = 28 so d = 28-q
0.1d + 0.25q = 5.50
0.10 * (28-q) + 0.25q = 5.50
2.80 - 0.10q + 0.25q = 5.50
0.15q = 5.50 - 2.80
0.15q = 2.70
q = 2.70 / 0.15
q = 18 quarters (she has)
50-18= 32 quarters (she needs)