A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using The population standard deviation is known to be 5 and the population distribution is normal.
Complete Question
A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using α=0.01. The population standard deviation is known to be 5 and the population distribution is normal.
[tex]H_o: \mu =28[/tex] versus H1: μ>28.
Round your answers to two decimal places.
[tex]z_{critical} =[/tex]
Answer:
[tex]z_{critical} = 2.33[/tex]
The observed value is [tex] z = 4.27 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 114
The sample mean is [tex]\= x = 30[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The population standard deviation is [tex]\sigma = 5[/tex]
The null hypothesis is [tex]H_o: \mu =28[/tex]
The alternative hypothesis is H1: μ>28.
Generally the test statistics (observed value ) is mathematically represented as
[tex] z = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } } [/tex]
=> [tex] z = \frac{ 30- 28 }{ \frac{5}{\sqrt{114} } } [/tex]
=> [tex] z = 4.27 [/tex]
From the normal distribution table the critical value of [tex]\alpha = 0.01[/tex] is
[tex]z_{critical} = 2.33[/tex]
-38 +(30) =
28 + 45 =
Answer:
I think the first answer is 8 and I dont know the second answer
Answer:
-38 + (-30) = -68
-28 + 45 = 17
This is a net of a square pyramid.
What is the surface area, in square centimeters, of the square pyramid?
Answer:
120cm
Step-by-step explanation:
The surface area of the square pyramid is 127.4 square centimeters
What is Three dimensional shape?A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The given figure is a square pyramid
The formula to find surface area = a²+2a√a²/4+h²
a is the base edge length and h is the height
a is 6 cm and h is 7 cm
Surface area = 6²+2(6)√6²/4+7²
=36+12√36/4+49
=127.4 square centimeters
Hence, the surface area of the square pyramid is 127.4 square centimeters
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Translate the phrase into an algebraic expression.
y more than 4
Answer:
y+4
Step-by-step explanation:
Help with number 1 please
Answer:
you could stay there 6 nights
Step-by-step explanation:
to solve this you would do 825$ ÷ by the amout which is 134$ and then you get 6.15671641791 then you would round it which give you 6 nights.
how to get domain and range from a table of values.
Answer: The domain is all of the possible values for the input (x) axis. The range is the possible values for the output (y).
Step-by-step explanation: You will have to subtract the least value from the greatest value for both your x and y.
What is (f + g)(x)?
f(x) = -2x
g(x) = 5x + 6
What is this written as a polynomial or a rational function
Answer:
(f + g)(x) = 3x + 6
Step-by-step explanation:
Brainliest?
helpppp?????????????
What is the slope of the line that goes through the points (1,-2) and (3,6)?
Question 1 options:
-4
4
1
2
Answer: 4
Step-by-step explanation: Brainliest plz!!
What is 34.567 rounded to the tenths place
Answer:
34.57 I'm pretty sure yayyy
Answer:
34.567 rounded to tenths is 34.6
Step-by-step explanation:
because if you look at the number to the right it five or more so you raise the score and the five turns to a 6 so 34.567 = 34.6
Consider a sample with data values of 27, 24, 21, 16, 30, 35, 28, and 24. Compute the 20th, 25th, 65th, and 75th percentiles. 20th percentile 1 1.8 Incorrect: Your answer is incorrect. 25th percentile 2 2.25 Incorrect: Your answer is incorrect. 65th percentile 3 5.85 Incorrect: Your answer is incorrect. 75th percentile
Answer:
20
21.75
27.85
29.5
Step-by-step explanation:
Arranging the values in ascending order we get
16 21 24 24 27 28 30 35
n = Number of values = 8
Rank is given by
[tex]\dfrac{\text{Percentile}}{100}\times (n+1)[/tex]
[tex]=\dfrac{20}{100}(8+1)=1.8[/tex]
Taking the fraction of the rank i.e., 0.8 and work out the weighted mean
[tex]0.8\times (21-16)+16=20[/tex]
The 20th percentile is 20
[tex]\dfrac{25}{100}(8+1)=2.25[/tex]
[tex]0.25(24-21)+21=21.75[/tex]
The 25th percentile is 21.75
[tex]\dfrac{65}{100}(8+1)=5.85[/tex]
[tex]0.85(28-27)+27=27.85[/tex]
The 65th percentile is 27.85
[tex]\dfrac{75}{100}(8+1)=6.75[/tex]
[tex]0.75(30-28)+28=29.5[/tex]
The 75th percentile is 29.5
How many groups of 10 milliliters are in 1-liter? Explain.
Answer:
100 GROUPS OF TEN
Step-by-step explanation:
THERE IS 1000 ML IN 1L
Solve for x? -10x-(-4)=14
Q: -10x-(-4)=14
A: x=-1
Process:
-Subtracting a negative is just like adding 10x+4=14
-Subtract 4 from both sides -10x=10
Divide -10 from both sides x=-1
I have a small dog and a big dog. My big dog weighs 50 pounds more than twice the weight of my small dog. The sum of their weght is 68 pounds. How much do they weigh?
Answer:
Small dog =18
Big dog=50
Step-by-step explanation:
68-50=18
Answer:
75+68
Step-by-step explanation:
An optical inspection system is used to distinguish among different part types. The probability of a correct classification of any part is 0.94. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. Determine the mean and variance of X.
Answer:
The mean and variance of X are 2.82 and 0.1692 respectively
Step-by-step explanation:
The binomial distribution is a discrete probability distribution that tells the percentage in which a result is likely to be obtained between two possibilities when performing n number of tests. In other words, a binomial distribution is a discrete probability distribution that describes the number of successes when conducting n independent experiments on a random variable.
In a binomial distribution, the mean indicates the mean value of a random phenomenon. It is calculated by:
μ=n*p
Where:
n is the number of trials p is the probability of successThis case is a binomial distribution, where n = 3 and p = 0.94. Then:
μ=3*0.94
μ=2.82
The mean of X is 2.82.
Variance is a measure of dispersion that represents the variability of a data series with respect to its mean. It is calculated by:
Var[X]= n*p*q
Where:
n is the number of trials p is the probability of success q is the probability of failureRemembering that the random variable X expresses the number of successes obtained when performing "n" independent Bernouilli tests or tests with probability "p" of success and "(1-p)" of failure, then q = 1-p.
So:
Var[X]= n*p*(1-p)
In this case:
Var[X]=3*0.94*(1-0.94)
Var[X]=3*0.94*0.06
Var[X]=0.1692
The variance of X is 0.1692
4- Employees at a certain company currently have to pay 7% of their health care costs,
while the company pays the rest. Next year, however, employees will have to pay 14%
of their health care costs. Express this change as:
absolute change (in percentage points) =
relative change =
Answer:
The absolute change would be 3 percentage points.
The relative change would be 100%
Step-by-step explanation:
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. For the group of 16, find the probability that the average percent of fat calories consumed is more than thirty-five (Round to 3 decimal places)
Answer:
Step-by-step explanation:
Mean μ = 36
standard deviation σ = 10
n = 16
standard deviation of the group σ₁ = σ / √n
σ₁ = 10/ √16
= 10 / 4 = 2.5
σ₁ = 2.5
P ( x > 35 ) = 1 - P ( x < 35 )
P ( x < 35 ) = P( z < (35 - 36) / 2.5 ) = P( z < (35 - 36) / 2.5 )
= P( z < 0.4 )
= .3446
P ( x > 35 ) = 1 - .3446
= .6554 .
Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
y-1=3(x+0)
y-0=3(x-1)
y+1=(1/3)(x+2)
y+2=(1/3)(x+1)
How can the point-slope form be written in function notation?
f(x)=(1/3)x-(5/3)
f(x)=(1/3)x-(1/3)
f(x)=3x-3
f(x)=3x+1
Answer: Use the graph of the line to answer the questions.
What is an equation of the line in point-slope form?
✔ y + 1 = (1/3)(x + 2)
How can the point-slope form be written in function notation?
✔ f(x) = (1/3)x – (1
You purchase 3 items for $4.23. About how much did you spend?
Answer:
4.23 rounded to the nearest whole number is 4.
Answer:
4.23 2.115 per item
Step-by-step explanation:
PLZZZ HELPS ME I WILL GIVE BRAINLIEST!
Which relations are functions?
Select Function or Not a function for each graph.
Answer: The first 3 are functions. The last one is not a function
Step-by-step explanation: What you can do is the line test. If you draw a line through it, the line shouldn't touch the arrow twice. Like the last one, it touches the line twice, so it is not a function
What is the probability that, for a random viewing of circuit boards 1 and 2, that the total number of defects observed will be at least 6
Answer:
0.3125
Step-by-step explanation:
From the full question in your book, the probability can be computed as:
[tex]P(X+Y=6) = P \{X=1,Y=5\} \cup \{X=2,Y=4\} \cup \{X=3,Y=3\} \cup \{X=4,Y=2\} \cup \{X=5,Y=1\}[/tex]
[tex]= P(X=1,Y=5) + P(X=2,Y=4)+P(X=3,Y=3)+P(X=4,Y=2)+P(X=5,Y=1)[/tex]
since all events are enclosed in brackets, they are mutually exclusives.
Then:
[tex]= P(X=1)P(Y=5)+P(X=2)P(Y=4)+P(X=3)P(Y=3)+P(X=4)P(Y=2)+P(X=5)P(Y=1)[/tex]
as X and Y are independent;
= [tex](0.25\times0.25 + 0.25\times0.25 + 0.25\times0.25+0.25\times0.25 + 0.25\times0.25)[/tex]
= 0.3125
Therefore;
P(X+Y= 6) = 0.3125
what is i^30
Math is killing me and i have no real help someone save me!!! I cant even start to understands this concept so if you could explain and give the answer that'd be great bunch of points if you do!!!
Answer:-1
Step-by-step explanation: It’s seen as a pattern going back and forth between a few answers.
Answer:
It's -1.
Step-by-step explanation:
i has no value but if you multiply it by itself 30 times you get -1. Imaginary numbers are great, I know.
A polynomial, P(x) = x2 + 2x + k has (x – 2) as a factor. What is
the value of k?
Answer:
x-2 =0
x=2
now
putting the x value in p
we have,
p(2) = x2 + 2x +k
= 2×2 +2×2+k
= 4+4+k
= 8+k
so,
Either
8+k =0
k= - 8
Someone help me I’ll give brainliest
Which statements are true? Select three options.
Karen owns a seafood restaurant. She orders trout from an online retailer
Each pound of trout costs $30, and the company charges a $2 fee for
shipping the order. However, if Karen orders 10 or more pounds, the trout
costs only $24 per pound, but the shipping fee is $6.
Which piecewise function models the cost of x pounds of trout?
30x + 2, 0 < x < 10
24x + 6, I > 10
24x + 6, 0 < x < 10
30.2 + 2, 3 > 10
O A. f(x) = {
O B. f(x) = {
O c. f(x) = {
O D. f(x) = {
{
24x + 6, 0 < x < 10
30.3 + 2, > 10
30x + 2,0 < X < 10
24x + 6, x > 10
Answer:
Step-by-step explanation:
In this problem we are required to provide the expression for the two scenarios highlighted
The first scenario is
"Each pound of trout costs $30, and the company charges a $2 fee for
shipping the order"
The expression for the above scenario is given as
30x + 2, 0 < x < 10
The second scenario is
"if Karen orders 10 or more pounds, the trout costs only $24 per pound, but the shipping fee is $6."
The expression for the second scenario is
24x + 6, x > 10
**WILL GIVE BRAINLIEST!
pre-calculus question, image attached
Answer:
Sorry, Don't know the answer.
Suppose the difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000. Determine the probability that the actual sale is within $1500 of the predicted sale (which means P(-1500
Answer: 0.375
Step-by-step explanation:
Given: The difference between actual and predicted weekly sales of a company follows a uniform distribution between -$4000 and $4000.
Probability density function: [tex]f(x)=\dfrac{1}{b-a}=\dfrac{1}{4000-(-4000)}=\dfrac{1}{8000}[/tex]
The probability that the actual sale is within $1500 of the predicted sale = [tex]\int^{1500}_{-1500}f(x)dx=\int^{1500}_{-1500}\dfrac{1}{8000}dx=\dfrac{1}{8000}[x]^{1500}_{-1500}\\\\= \dfrac{1}{8000}(1500-(-1500))\\\\= \dfrac{1}{8000}(3000)=0.375[/tex]
Hence, Required probability =0.375
find the intercepts and graph each line x + 3y = -4
Answer:
The x intercept is -4
And y intercept is -4/3
Which of the systems of equations below is equivalent to the system shown?
4x + 5y = 3
2x + 3y = 1
Ο Α.
4x + 5y = 3
- 4x - 5y = 2
ОВ.
12x + 15y = 9
- 12x + 18y = 6
O C.
4x + 5y = 3
- 4x - 3y = 1
OD.
12x + 15y = 9
- 12x - 18y = -6
The system of equations is Option D.
12x + 15y = 9
-12x - 18y = -6
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be A , 4x + 5y = 3
Let the second equation be B , 2x + 3y = 1
Now ,
The equations can be solved by
4x + 5y = 3 be equation (1)
2x + 3y = 1 be equation (2)
Multiply equation (1) by 3 , we get
12x + 15y = 9 be equation (3)
Multiply equation (2) by -6 , we get
-12x - 18y = -6 be equation (4)
So , the system of equations are
A , 12x + 15y = 9
B , -12x - 18y = -6
Hence , the system of equations are 12x + 15y = 9 and - 12x - 18y = -6
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Order the values from least (top) to greatest (bottom). -|21|, -16, |-10|, 22, |-32|
Answer:
22
-10
-16
-21
-32
Explanation:
On a number line, negative numbers are on the left and positive numbers are on the right. So, typically, the positive numbers would be less than the negative numbers.
Hope this Helps!