Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.a. If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 9 pins is at least 51?b. Without assuming population normality, what is the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51?
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
Help!? Helping my son with geometry ... I have no clue what I’m doing here
We are Given:
∠1 = 65°
Finding the measure of all other angles with proof:∠2:
∠1 + ∠2 = 180° (angle 1 and 2 form a Linear Pair)
65 + ∠2 = 180 (Angle 1 = 65°)
∠2 = 180 - 65
∠2 = 115°
∠3:
∠1 = ∠3 (Angle 1 and 3 are vertically opposite)
65 = ∠3 (Angle 1 = 65°)
∠3 = 65°
∠4:
∠4 = ∠2 (Vertically opposite angles)
∠4 = 115° (∠2 = 115°)
∠5:
∠5 = ∠1 (Corresponding angles)
∠5 = 65° (∠1 = 65°)
∠6:
∠6 = ∠2 (Corresponding angles)
∠6 = 115° (∠2 = 115°)
∠7:
∠7 = ∠3 (Corresponding Angles)
∠7 = 65° (∠3 = 65°)
∠8:
∠8 = ∠4 (Corresponding angles)
∠8 = 115° (∠4 = 115°)
If y = -6 when x = 16, find y when x = 8.
Answer:
y=-3
Step-by-step explanation:
16/2=8
-6/2=-3
Answer:
-3
Step-by-step explanation:
I think this -6/16 = -3/8 divided both sides by 2
A high school coach wants to buy new shirts for the 25 members of the track team. The coach must spend less than $300 on the shirts and needs to figure out how much he can spend per shirt, s.
Which of the following must be true about the inequality and the resulting graph? Select three options.
The inequality should be written as 25 s less-than 300.
The inequality should be written as 25 s greater-than 300.
The circle is open.
The circle is closed.
The arrow points left.
The correct options are 1, 3 and 5.
Step-by-step explanation:
Let the price of a new shirts be s.
The number of members is 25. The price of 25 shirts is 25s.
The cost must be less than $300. It means
Therefore option 1 is correct.
Divide both sides by 25.
The sign of inequality is < instead of ≤. It means the 12 is not included in the solution set.
Open circle is used for "<" and ">". Closed circle is used for "≤" and "≥".
Since the sign of inequality is <, therefore the circle is open and option 3 is correct.
The value of s is less than 12.
Therefore the arrow points left and option 5 is correct.
Answer:
A,C,E
Step-by-step explanation:
i got it right on edge 2021
Where did the student go wrong?
i will give brainilest
The table shows the number of each score earned by 120 students on a sixth grade mathematics test.
Score Number of Students
100 9
95 18
90 72
85 15
80 6
What is the ratio of students scoring above 80 to students scoring exactly 80 on this test?
Group of answer choices
1 to 20
19 to 1
1 to 19
20 to 1
3x+5=23 what is the value of x?
Answer:
X = 6
Step-by-step explanation:
Hope this helps!
....
what is the sum of (-2.1x + 3.7) and (5 + 4.9x)?
Answer: [tex]=2.8x+8.7[/tex]
[tex]=-2.1x+3.7+5+4.9x[/tex]
[tex]=(-2.1x+4.9x)+(3.7+5)[/tex]
[tex]=2.8x+8.7[/tex]
Chaz kept a record of how many gallons of gas he purchased each day last week. Drag and drop the days into the correct boxes to order the days from the least amount of gas Chaz purchased to the greatest amount of gas Chaz purchased.
Day Gas (in gallons)
Monday 4.5
Tuesday 3.6
Wednesday 4.252
Thursday 3.71
Friday 4.255
Answer:
The arrangement of days from least to greatest according to number of gallons is:
Tuesday
Thursday
Wednesday
Friday
Monday
Step-by-step explanation:
The given amount of gallons is in decimal form and we have to arrange the numbers in the order from least to greatest.
4.5 is the largest number in the given numbers.
Then comes 4.252 and 4.255
As 0.252<0.255 so 4.252 will be smaller.
The smallest number is 3.6
Arranging the numbers, we get
3.6
3.71
4.252
4.255
4.5
Now arranging the corresponding day to each number,
The arrangement of days from least to greatest according to number of gallons is:
Tuesday
Thursday
Wednesday
Friday
Monday
Calculate the average rate of change from 3 to 9 seconds, in feet per second
Answer:
D is the Answeer
Step-by-step explanation:
Average rate of change from 3 to 9 seconds is -0.475 feet per second
What is Average rate of change?It is a measure of how much the function changed per unit, on average, over that interval
Given,
P(t) represents the height in feet and t represents the time in second
At t= 3 second, P(t) = 6.26 feet
At t=9 second, P(t) = 3.41 feet
Average rate of change = [tex]\frac{P(b)-P(a)}{b-a}[/tex]
Substitute the values in the equation
Average rate of change = [tex]\frac{P(9)-P(3)}{9-3}[/tex]
[tex]=\frac{3.41-6.26}{9-3}\\=\frac{-2.85}{6}\\[/tex]
= -0.475 feet per second
Hence, the Average rate of change from 3 to 9 seconds is -0.475 feet per second
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round 688. to the nearest hundred. Enter your answer in the box below.
Answer:
700
Step-by-step explanation:
thats the answer ik
Answer:
700
Step-by-step explanation:
688 is closer to 700 than 600 so it is rounded to 700
Write sin(x+1) in terms of unshifted sine and cosine. Write your answer using decimals.
Please provide explanation, I’m confused.
Answer: sin(x + 1) = 0.841*cos(x) + 0.540*sin(x)
Step-by-step explanation:
Here we can use the relation:
Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
In this case we have:
sin(x + 1)
This means that the graph of sin(x) is shifted one unit to the left.
But we can write this, using the above relation, as:
sin(x + 1) = sin(x)*cos(1) + sin(1)*cos(x)
Now we have no longer a shift, and we can replace:
sin(1) = 0.841
cos(1) = 0.540
Then:
sin(x + 1) = 0.841*cos(x) + 0.540*sin(x)
Can the following question be considered a statistical question and why or why not?
Do students at Bryan Middle School exercise?
Yes, it specifies the population
No, it does not specify the population
Yes, it anticipates enough variability in responses
No, it does not anticipate enough variability in responses
Answer: Yes, it anticipates enough variability in responses
Step-by-step explanation:
A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.
The area of the postcard pictured below is 24 square inches. What is the width b of the message section (in inches)? Pick the equation that would best model this situation.
A. 4(b + 3) = 24
B. 3(4 + b) = 24
C. 4(b - 3) = 24
D. 3(b - 4) = 24
Answer:
Step-by-step explanation:
4(b + 3) = 24
Answer:
A. 24 = 4(b + 3)Step-by-step explanation:
Area is equal to length times width. In this case, the length is b + 3 (since both b and 3 are part of the width, with the length being 4.
Substitute into the equation for area:
a = lw
a = 4(b + 3)
The area is 24, so the final answer is:
A. 24 = 4(b + 3)Anyone wanna be freinds
Answer:
yes
Step-by-step explanation:
Answer:
sure......................................
Which number sets (i.e. Natural, Whole, Integer, Rational, Real, etc.) are best suited to represent discrete functions? Why? Which number sets are best suited to represent continuous functions? Why?
Answer:
They are considered discrete
Step-by-step explanation:
because
If the number of dates Anna and John had is represented by three consecutive integers, what is the algebraic expression for
the total number of dates they have had?
Step-by-step explanation:
x,x+1,x+2
Topic: algebraic expression
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Mr mogi barrowed $9,000 for 10 years to make home improvements if he paid a total of $11,000 in interest in interest at what I test rate did he barrow the money
Answer:
Step-by-step explanation:
Multiply 3 over 7 times 5over 8
Answer:
0.26785714285
Step-by-step explanation:
Answer:
Step-by-step explanation:
3/7 * 5/8
This equates to 15/56.
Multiply 3 and 5 (which equals 15).
Multiply 7 and 8 (which equals to 56)
#teamtrees #WAP (Water And Plant)
Which figure is shown in the drawing?
ray XY is the answer
Please give Brainliest also I hope this helps!
In the figure, of the given alternatives, a ray XY is shown.
What is a ray?The definition of ray in math is that it is a part of a line that has a fixed starting point but no endpoint. It can extend infinitely in one direction.Given is the figure as shown in the image.
Of the given options, only a ray given by XY{with overhead arrow} can be seen as it has one starting point at [x] and extends along.
Therefore, in the figure, of the given alternatives, a ray XY is shown.
To solve more questions on geometry, visit the link below -
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5r + 2d
I need to know the answer to this equation.
R = 3 and d = 5
brainliest and 30 points for correct answer and first person ONLY
Answer:
=25
Step-by-step explanation:
plug in the numbers for the variables
5(3)+2(5)
15+10
25
what is the variance of the following set of data? 5 ,55 , 505, 255, 5, 75 , 85, 65
Answer:
27964.286
Step-by-step explanation:
i just used calculator soup
Answer:
28,912
Step-by-step explanation:
i also used calculator soup but gave the right answer
Nina likes to tip restaurant staff 18% when she enjoys the meal and has good service. Which expression represents the amount of tip, in dollars, that Nina will give when she has a positive experience eating a meal that cost n dollars? 0.18n 18n StartFraction n over 18 EndFraction n + 0.18
Answer:
18n
Step-by-step explanation:
just got done taking the test
Answer:
0.18n
Step-by-step explanation:
identify this lobe and y-intercept of the line given by y equals to 4 x - 3
Answer:
Slope = 4
y-intercept = -3
Step-by-step explanation:
A slope describe the steepness of a graph, which can also be referred to as gradient. The general equation of a linear graph is given as:
y = mx ± c
where: m represents the slope of the graph and c the intercept on the required axis.
Given: y = 4x - 3
Comparing this equation with the general equation of a linear graph, it can be observed that; the slope is 4, while the intercept on the y axis is -3.
Thus,
slope = 4
intercept on the y axis = -3
Write 0.0000000068 as a scientific notation
Answer:
10×6.8 to the 9th power
PLZ HURRY IT'S URGENT!!!!
Represent the situation as a system of equations.
Rent a Truck rents a moving truck for $40.00 and $0.20 per mile.
Moving R Us rents the same moving truck for $1.00 per mile but with no upfront charge.
Let x represent the number of miles traveled.
Question 5 options:
y=40x+0.20 y=x+1
y=0.20x+40 y=x+1
y=40x+0.20 y=1.00x
y=0.20x+40 y=1.00x
Answer:
y=0.20x+40; y=1.00x
Step-by-step explanation:
Company 1 is charging upfront and then after u have a unknown variable for how many miles you drive. Company 2 is only charging you 1.00$ per mile driven and depending on how many miles you drove will depend on how much you will pay.
Matteo is following this recipe to mak
a cake.
He wants to make three of these
cakes.
How much of each ingredient does he
need?
Recipe: Makes 1 cake
6 ounces butter
5 ounces sugar
7 ounces of flour
3 eggs
2 teaspoons (tsps) baking powder
Pls help me I'm trying too sleep and they keep sending me homework
Answer:
Below is the step by step explaination of the procedure
Step-by-step explanation:
So since he wants to make three cakes we will multiply the recipe by 3 to get the amount of ingredients this person will need.
6*3 = 18 ounces of butter
5*3 = 15 ounces of sugar
7*3 = 21 ounces of flour
3*3 = 9 eggs
2 * 3 = 6 teaspoons of baking powder.
How does the value of c affect the graph of f(x) = et+c?
Answer: A
Step-by-step explanation: c shifts the graph up or down.
Simplify the following expression by combining like terms:
7f + 8g + 4f + 3f + 6f + 2g
Answer:
20f + 10 g or 10(2f + g)
Step-by-step explanation:
7f + 4f + 3f + 6f = 20f
2g + 8g = 10g
PLS MARK BRAINLIEST
Answer:
20f+10g
Step-by-step explanation: That was actually really easy
Which exponential expression represents the numerical expression 9⋅9⋅9?
93
39
3×9
9×3
Answer:
93
Step-by-step explanation:
Answer: The first one 9³
Step-by-step explanation:
Note: 9³ or nine to the third power or 9-cubed is correct, because we are multiplied the number 9 by itself, three times
The value equal to:
9*9*9 is equal to: 9³
that is, nine to the THIRD power or:
nine to the power of three