The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 117 chips. (a) Determine the 28th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 97% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate
Answer:
Using z score formula:
X = z ∂ + µ
= 157.833
Step-by-step explanation:
Solution:
Mean = µ = 1262
Standard deviation = ∂ = 117
(a) 28th percentile for the number of chocolate chip.
P( z < z) = 28%
= 0.28
P( z<- 0.58) = 0.28
Z = -0.58
By using z score formula:
Z = x - µ /∂
-0.58= x – 117 / 1262
X = (- 0.58)(117) + (1262)
= 1194.14
(b) Middle 97% of bag.
P(-z < z < z) = 97%
= 0.97
P( z < z) – p(z < -z) = 0.97
2p(z < z) -1 = 0.97
2p (z < z) = 1 + 0.97
P(z < z) = 1.97 / 2
= 0.99
P(z < 2.33) = 0.99
Z ± 2.33
By using z score formula:
Z = x - µ / ∂
X = z ∂ + µ
= - 2.33 x 117 + 1262
=989.39
Z = 2.33
X = z ∂ + µ
= 2.33 x 117 + 1262
=1533.61
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate.
By using standard normal table,
The z dist’n formula:
P(z < z ) = 25%
=0.25
P(z < -0.6745) = 0.25
Z = 0.6745
Using z score formula:
X = z∂ + µ
= - 0.6745 x 117 + 1262
= 1183.0835
First quartile = Q1 =1183.0835
The third quartile is:
P(z<z) = 75%
= 0.75
P(z < 0.6745) = 0.75
Z = 0.6745
Using z score formula:
X = z ∂ + µ
= 0.6745 x 117 + 1262
= 1340.9165
IQR = Q3 – Q1
= 1340.9165 – 1183.0835
= 157.833
gimme stuff to improve on or just things to draw :)
Answer:
draw your representation of a 4 characters depicting each Hogwarts house?
Answer:
hmm you are already really good, I'm not sure if you have already but try drawing different perspectives of the head/ neck :)
A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1664 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 206 149
Dorm 295 276
With Parent(s) 55 68
Sorority/Fraternity House 132 204
Other 180 99
What is the probability that a customer is female and lives in a dorm or is female and lives in 'Other'? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer: 0.2254
Step-by-step explanation:
Let E= Event of getting of female lives in a dorm.
F = Event of getting of female lives in a 'Other'.
From the table , n(E) = 276 and n(F) = 99
and n(E∩F) = 0 [E and F are Mutually exclusive]
Now, n(E∪F)= n(E) + n(F) - n(E∩F)
= 276+99-0
= 375
also, n(S) =1664 (Sample size)
Required probability : [tex]P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}[/tex]
[tex]=\dfrac{375}{1664}\approx0.2254[/tex]
Hence, the probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254
In a circle with a radius of 3 ft, an arc is intercepted by a central angle of 120 degrees.
What is the length of the arc?
Answers:
6.28 ft 09.42 ft
18.84 ft
28.26 ft
Answer:
A) 6.28ft
Step-by-step explanation:
r = 3ft
θ = 120°
Arc length = θ ⋅ (2πr/360)
Arc length = 120° ⋅ (2π ⋅ (3/360))
6.2831853
i hope this explains it, pls mark brainliest
What is the length of a segment with endpoints at F(6, 4) and G(14, 19)? Round to the nearest whole number.
Answer:
17
Step-by-step explanation:
d = √( (x₂ - x₁)² + (y₂ - y₁)² )
= √( (14 - 6)² + (19 - 4)² )
= √( 8² + 15² )
= √( 64 + 225 )
= [tex]\sqrt{289}[/tex]
= 17
A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x. What is the value of y? 3 4 5 6
Answer: y=3
Step-by-step explanation:
Since the quadrilateral has 90 degree angles, it must be a a square or a rectangle. This means the measure of sides left and right are the same and the measure of sides top and bottom are the same.
To get the measure of y, you can use left and right or top nd bottom.
I'll use left and right. 10=2y+4 => 10-4=2y => 6=2y => y=3
You can check it by substituting. 2(3)+4=10 The answer is the measure of the right side, which is the same as the measure of the left side.
I hope this helps you!
Answer:
3
Step-by-step explanation:
PLEASE HELP I CANT DO MATH
Answer:
c
Step-by-step explanation:
the number line says less than 4 so if you solce for all the equations c will be x<4
6x(24÷2) equals what?
Answer:
72
Step-by-step explanation:
do 24/2=12x6=72
The output from the machine depends on the input to to
A.
B.
C.
D.
Answer:
i think its B
Step-by-step explanation:
Breanna thought of a number, added 7 to it, subtracted 6 from it, added 7 to her answer, and then subtracted 6 from her answer. She got a final number of 13. What was her starting number
Answer:
the answer is definitely 11
Step-by-step explanation:
Joey made this
graph to show how many incorrect
answers students got on a test. how
many students got 3 answers incorrect?
how do you know?
number of students
Answer:
4 students got three answers incorrectly.
The number of students got 3 answers incorrect is 4.
What is histogram?A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.
Now from the given histogram following informations are extracted-
Number of students got 1 answer incorrect = 2
Number of students got 2 answer incorrect = 3
Number of students got 3 answer incorrect = 4
Number of students got 4 answer incorrect = 1
Number of students got 5 answer incorrect = 2
Thus from above we can conclude that,
Number of students got 3 answer incorrect = 4
Thus, the number of students got 3 answers incorrect is 4.
To learn more about histogram :
brainly.com/question/1593386
#SPJ2
A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. What is the Probability of two or more questions right? X 0 1 2 3 P(X) .1875 .4375 .3125 .0625
Answer:
[tex]P(X\geq 2) = 0.375[/tex]
Step-by-step explanation:
Given
X ------0 --------1 -------- 2--------- 3
P(X) --.1875 -.4375 ---.3125 --- .0625
Required
Determine [tex]P(X\geq 2)[/tex]
This is calculated as:
[tex]P(X\geq 2) = P(X = 2) + P(X = 3)[/tex]
[tex]P(X\geq 2) = 0.3125 + 0.0625[/tex]
[tex]P(X\geq 2) = 0.375[/tex]
Find the missing side of the given right triangle. *
7
9
Х
Pythagora's theorem can be used to solve problems like this
Let A and B be events with P(A) = 0.7 and P(A ∩ B) = 0.3. For what value of P(B) will A and B be independent?
Answer:
The value of P(B) for independent events = 0.429
Step-by-step explanation:
Given;
P(A) = 0.7
P(A ∩ B) = 0.3
A and B will be independent if event A will occur and B will also occur, ie A and B will occur independently.
P(A) and P(B) = P(A ∩ B)
[tex]P(B) = \frac{ P(A\ n\ B) }{P(A)}\\\\ P(B) = \frac{0.3}{0.7}\\\\P(B) = 0.429[/tex]
Therefore, the value of P(B) for independent events = 0.429
Rewrite the following without an exponent:
4^-4. (-4 is the exponent).
Thank you!
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
The [tex]4^{-4}[/tex] without exponents is 1/256.
Given,
[tex]4^{-4}[/tex]
We need to write the given expression without exponents.
What are exponents?
Exponents are power to a base value.
Example:
a² and b³
a and b are base
2 and 3 are exponents.
We can a fraction into an exponents form and vice versa.
Example:
1/a = [tex]a^{-1}[/tex]
We have,
[tex]4^{-4}[/tex]
Changing into a fraction form
= 1/[tex]4^{4}[/tex]
Find [tex]4^{4}[/tex].
[tex]4^{4}[/tex] = 4 x 4 x 4 x 4 = 16 x 16 = 256
Now,
= [tex]4^{-4}[/tex]
= 1/[tex]4^{4}[/tex]
= 1/256
We get,
= 1/256
Thus the [tex]4^{-4}[/tex] without exponents is 1/256.
Learn more about exponents of a cube number here:
https://brainly.com/question/15993626
#SPJ2
Rewrite each of the following numbers
as a square or a cube of some other
number.
0.064
Please solve and explain this...
Answer:
Correct option: c. 8
Step-by-step explanation:
One-sided Limit
Given a piecewise function, we can find the limit when the variable approaches a specific value in the boundary of two pieces.
Special care must be taken to determine what function will be used to calculate the limit according to the conditions of the independent variable.
The given function p(t) has 3 pieces or subfunctions according to different conditions of t. We need to calculate:
[tex]\lim _{x\to 2^{-}}p(t)[/tex]
We must find the subfunction where a value of t is close to 2 but is less than 2.
The correct subfunction is
[tex]p(t)=t^3\qquad -2\le t\le 2[/tex]
Taking the limit:
[tex]\lim _{x\to 2^{-}}p(t)=\lim _{x\to 2}t^3=2^3=8[/tex]
Correct option: c. 8
You are planning to evaluate the mean of a single continuous variable from a study with a sample of n =10 using the t statistic. What are the degrees of freedom for the sample?a. 11b. 9c. 10d. 8With another study, where you also plan on evaluating a mean using the t statistic, you have sample of n =31 that has as SS of 120. What is the variance for the sample?a. 10.95b. 14,400c. 4d. 2.00For a sample of n =25 that has a sample variance of 400, what is the estimated standard error for the sample?a. 16b. 17c. 4.08d. 4
Answer:
a) b. 9
b) c. 4
c) d. 4
Step-by-step explanation:
You are planning to evaluate the mean of a single continuous variable from a study with a sample of n =10 using the t statistic. What are the degrees of freedom for the sample?a. 11 b. 9 c. 10 d. 8
The formula for degree of freedom
= n - 1
n = 10
Degrees of freedom for the sample = 10 - 1
= 9
Option b is correct.
b) With another study, where you also plan on evaluating a mean using the t statistic, you have sample of n =31 that has as SS of 120.
What is the variance for the sample?a. 10.95 b. 14,400 c. 4 d. 2.00
The formula for Variance of a samples = SS(Sum of squares) /n - 1
n = 31
Variance of samples = 120/31 - 1
= 120/30
= 4
Option c is correct
c) For a sample of n =25 that has a sample variance of 400, what is the estimated standard error for the sample?a. 16 b. 17 c. 4.08 d. 4
The formula for standard error =
Standard deviation/√n
We are given Sample variance.
Standard deviation = √400
= 20
Hence, Standard Error = 20/√25
= 20/5
= 4
Option d is correct.
a) The degrees of freedom for the sample is option b. 9.
b) The variance is option c. 4.
c) The standard error is option d. 4.
Calculation of the degree of freedom, variance, and the standard error:a.
The formula for degree of freedom
= n - 1
n = 10
Now
Degrees of freedom for the sample should be
= 10 - 1
= 9
b) The variance should be
Since
n = 31
So,
Variance of samples = 120/31 - 1
= 120/30
= 4
c.
The formula for standard error is
= Standard deviation/√n
Here,
Standard deviation = √400
= 20
so, Standard Error = 20/√25
= 20/5
= 4
Learn more about variance here: https://brainly.com/question/24138432
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.45cm and a standard deviation of 0.4cm. Using the empirical rule, what percentage of the apples have diameters that are greater than 7.85cm? Please do not round your answer.
Answer:
The percentage is 68.26%
Step-by-step explanation:
Before we use the empirical rule , we need to find the value of the z-score
Mathematically;
z-score = (x - mean)/SD
Thus;
z-score = (7.85 - 7.45)/0.4 = 0.4/0.4 = 1
So the percentage we want to calculate now is the percentage of values within 1 standard deviation of the mean
According to the empirical rule, 68.26% of values are within 1 standard deviation of the mean
Customers arrive to a bank according to a Poisson process having a rate of 8.6 customers per hour. Suppose we begin observing the bank at some point in time. (a) What is the probability that 3 customers arrive in the first 30 minutes
Answer:
The value is [tex]P(X = 3) = 0.1798[/tex]
Step-by-step explanation:
From the question we are told that
The rate is [tex]\lambda = 8.6 \ hr ^{-1}[/tex]
General probability distribution for Poisson distribution is mathematically represented
[tex]P(X = x) = \frac{(\lambda * t)^{x} }{x!} * e^{-\lambda * t}[/tex]
Given that is in per hour then the unit of t is in hours
Generally 30 minutes = [tex]0.5 \ hours[/tex]
Generally the probability that 3 customers arrive in the first 30 minutes is mathematically represented
[tex]P(X = 3) = \frac{( 8.6 * 0.5 )^{3} }{3!} * e^{-8.6 * 0.5 }[/tex]
=> [tex]P(X = 3) = 0.1798[/tex]
Confused on this please help
Answer: it would be half the size
Step-by-step explanation:
Find the value of x in the triangle shown below. x = 56° 99°
Answer:
x = 25 degrees
Step-by-step explanation:
All angles in a triangle should add up to 180 degrees. So to solve for x, set up an equation where all three angles added up equals 180.
180 = 99 + 56 + x
180 = 155 + x
25 = x
The unknown angle is equal to 25 degrees.
Does anyone know this stuff? Im bad at it
Answer:
6
Step-by-step explanation:
The Daily Info charges a fee of $650 plus $80 per week to run an add. The People's Paper charges $145 per week. For how many weeks must an ad run for the total cost at the Daily Info to be less expensive than the cost at the People's Paper?
Answer:
10 weeksStep-by-step explanation:
let the total cost be y
and let the number of weeks be x
Daily Info charges
y=650+80x---------1
People's Paper charges
y=145x---------------2
equating 1 and 2 to solve for x we have
650+80x=145x
650=145x-80x
650=65x
x=650/65
x=10
Therefore the answer is 10 weeks
Solve for x , Help asap
Answer:
x = -3.5
Step-by-step explanation:
Mark brainliest please!!
match the angle with it's corresponding classification
Answer:
∠TPR = right angle
∠SPQ = acute angle
∠QPT = obtuse angle
Step-by-step explanation:
Right angles are 90°, acute angles are angles less than 90°, obtuse angles are angles more than 90°
Graph the line passing through (-6,-3) whose slope is m=2
Answer:
Start at (−6,−3) and count up 2 units and right 1 unit to find a second point. Connect the two points with a line to find the graph.
Step-by-step explanation:
Start by plotting the point (−6,−3). Use the slope formula m=rise/run to identify the rise and the run.
m=2
rise/run = 2/1
rise = 2
run = 1
Start at (−6,−3) and count up 2 units and right 1 unit to find a second point. Connect the two points with a line to find the graph.
Write the expression as a monomial in standard form.
(−3xy^2)^3 · (-2/3x^2y^3)^4
Answer:
It would be -16/13x^11y^18.
The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is
-16 /3[tex]$ x^5y^6[/tex]
What is meant by standard form?A number in standard form in mathematics. Standard decimal numbers are the easiest to read and write. For example, the standard form of the decimal number 0.007 is 7 10-3. It can be difficult to read or write very large or very small numbers. As a result, we write them in standard format. Any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten is said to be in standard form.An equation is written in standard form as Ax + By = C, where A, B, and C are all integers. This form of the equation is especially useful for calculating the x- and y-intercepts.Given,
[tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(-3 x y^2\right)^3:-27 x^3 y^6 \\[/tex]
[tex]&=-27 x^3 y^6\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(\frac{-2}{3 x^2 y^3}\right)^4: \frac{16}{81 x^8 y^{12}} \\[/tex]
[tex]&=-27 x^3 y^6 \frac{16}{81 x^8 y^{12}}[/tex]
Apply the fraction rule:
[tex]$\quad a \cdot \frac{b}{c}=\frac{a \cdot b}{c}$[/tex]
∴ [tex]=-\frac{27 x^3 y^6 \cdot 16}{81 x^8 y^{12}}[/tex]
Factor the number: 81 = 27.3
[tex]=-\frac{27 x^3 y^6 \cdot 16}{27 \cdot 3 x^8 y^{12}}[/tex]
Cancel the common factor: 27
[tex]=-\frac{x^3 y^6 \cdot 16}{3 x^8 y^{12}}$$[/tex]
Simplify
[tex]$\frac{x^3}{x^8}: \frac{1}{x^5}$[/tex]
∴ [tex]=-\frac{y^6 \cdot 16}{3 x^5 y^{12}}[/tex]
Simplify the equation,
[tex]$\frac{y^6}{y^{12}}: \frac{1}{y^6}$[/tex]
then we get,
[tex]=-\frac{16}{3 x^5 y^6}[/tex]
Hence, The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is -16 /3[tex]$ x^5y^6[/tex]
To learn more about standard form, refer to:
https://brainly.com/question/187506
#SPJ2
the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat
Answer:
450
Step-by-step explanation:
First we have to find the discount
20% of 1500 = 300
if you search up 20 x 1500/100, it would say 300
you can do that same equation in your maths book, and also by canceling out
10% vat tax
so 10% of 1500 = 150
since it is tax, we have to add it to our discount
300 + 150 = 450
450 is the answer
Why are the triangles below congruent?
Answer:
SSS
Step-by-step explanation:
We know this triangles are congruent due to SSS because AB is congruent to CD because of the tick marks. AB is also congruent to BC due to the tick marks. BD Is congruent to BD by the reflexive property. Therefore, triangle ADB is congruent to triangle CDB by SSS.
Please mark brainliest if this helped you :)
Answer:
SSS
Step-by-step explanation: