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A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that whenever this process is in control, package weight is normally distributed with a mean of 20 ounces and a standard deviation of two ounces. Each day last week, he randomly selected four packages and weighed each Day Weight (ounces) Monday 23 22 23 24 Tuesday 23 21 19 21 Wednesday 20 19 20 21 Thursday 18 19 20 19 Friday 18 20 22 20 If he uses upper and lower control limits of 22 and 18 ounces, what is his risk (alpha) of concluding this process is out of control when it is actually in control (Type I error)
Using the normal distribution and the central limit theorem, it is found that his risk is of 0.0456.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], 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 20 ounces and standard deviation of 2 ounces, hence [tex]\mu = 20, \sigma = 2[/tex].Sample of 4 packages, hence [tex]n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]The risk is the probability of being more than 2 ounces from the mean, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Applying the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2}{1}[/tex]
[tex]Z = 2[/tex]
The risk is P(|Z| > 2), which is 2 multiplied by the p-value of Z = -2.
Looking at the z-table, Z = -2 has a p-value of 0.0228.0.0228 x 2 = 0.0456
The risk is of 0.0456.
For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
can u answer this plz thanks
Answer: 3/4 of 8 just means 3/4 x 8, which is 6 miles. Do the same with 3/5 x 10, which is also 6 miles. Therefore both of them walked the same distance. Please mark me brainliest!
4-0,9+(-0,11)-(-1,3) PLEASE HELP
Answer:
-20
Step-by-step explanation:
PEMDAS
Please help me solve this!
We know that the sample standard deviation is 10 and the sample size is 70. For what sample mean would the ������ -value be equal to 0. 05? assume that all conditions necessary for inference are satisfied.
PLEASE HELP (TEST) The graphs below show measurements from cubes with
different side lengths.
Which pairs of variables have a linear relationship?
Select two options.
24
O side length and perimeter of 1 face
20
O perimeter of 1 face and area of 1 face
O surface area and volume
Perimeter of 1 Face
A.
U area of 1 face and surface area
O side length and volume
4
2.
1
3
4
5
6
X
Side Length
40
AB
36
32
Answer:
do you still need the answer?
Step-by-step explanation:
ITO
Jacky starts biking to meet up with her friend. She knows that if she bikes at a speed of
10 mph he will be 3 minutes late for the meeting. Jacky also knows that if she bikes at a
speed of 12 mph, she will be there 2 minutes before they agreed to meet. How much
time does she have left before the appointed time?
Using the speed - distance relationship, the time left before the appointed time is 27 minutes.
Recall :
Distance = speed × time Let time = tAt 10mph :
Distance = 10 × (t + 3) = 10t + 30 - - - (1)At 12 mph :
Distance = 12 × (t - 2) = 12t - 24 - - - - (2)Equate (1) and (2) :
10t + 30 = 12t - 24
Collect like terms
10t - 12t = - 24 - 30
-2t = - 54
Divide both sides by - 2
t = 54 / 2
t = 27
Hence, the time left before the appointed time is 27 minutes.
Learn more : https://brainly.com/question/25669152
Answer:
7
Step-by-step explanation:
Please no "files": Simplify. Express your answer as the given base raised to a single exponent.
(9^6)^8
Answer:
9^48
Step-by-step explanation:
when parenthesis are involved, you multiply the powers
6*8=48
Laura is training to run a race. She keeps track of the number of miles she runs. She has been training for 5 weeks, and she has run a total
of 40 miles. At what rate has she been running, in miles per week?
Answer:
8 miles per week!
Step-by-step explanation:
40 miles / 5 weeks = 8!
so it would be 8 miles per week.
i hope this helps!!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x + 6y = -54
Answer:
y = - 4/3x - 9
Step-by-step explanation:
Answer:
[tex]y = -\frac{4}{3}x - 9[/tex]
Step-by-step explanation:
The standard form of linear equation is: Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.
Given the linear equation in standard form, 8x + 6y = -54, we can transform this equation into its slope-intercept form, y = mx + b.
First, subtract 8x from both sides:
8x + 6y = - 54
8x - 8x + 6y = - 8x - 54
6y = -8x - 54
Divide both sides by 6 to isolate y:
[tex]\frac{6y}{6} = \frac{-8x - 54}{6}[/tex]
[tex]y = -\frac{4}{3}x - 9[/tex] ⇒ This is the slope-intercept form where the slope, m = [tex]- \frac{4}{3}[/tex], and the y-intercept, b = -9.
What is the order of operations in math.
1. Order each set of numbers from least to greatest.
a) 23 405, 23 100, 680 155, 680 056, 607 463
b) 320 376, 409 217, 317 758, 329 000, 320 768
help please !!!!!!!!!!!!!
Answer: + or - 8
Step-by-step explanation:
A. x^2 could be represented by the area of a square. Length and width are the same, so the area would be x^2. The answer is clearly wrong, since a square with sides of 32 would create a much larger area than 64.
B. x^2 = 64
What number times itself equals 64? = 8
This could be either positive or negative, since (-8)^2 is also equal to 64.
What is the other endpoint of the segment with midpoint (-3) and endpoint (-7)?
O 4
O 1
0-11
0-5
Answer:
1
Step-by-step explanation:
From -3 to -7 the distance is 4 (-3--7=4). Midpoint means that point -3 bisects the segment into two equal parts. So, the other endpoint is 4 units away from -3. Since -3+4=1, 1 is answer.
A sno-cone machine priced at $140 is on sale for 20% off. The sales tax rate is 6%. What is the price of the sno-cone machine after the discount and sales tax?
A) $112.00
B) $118.72
C) $28.00
D) none of the above
Answer:
118.72
Step-by-step explanation:
I just used my calculator 0-0 hope this helped :)
How to take inverse of a matrix.
Step-by-step explanation:
I hope this is your answer
Answer:
k;bjkbihpkbk
Step-by-step explanation:
How to multiple decimals by decimals.
Answer:
To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Put the following decimals in order from
least to greatest
{0.067, 0.06, 0.007, 0.09, 0.0076)
A company that makes hair-care products had 8,000 people try a new shampoo. Of the 8,000 people, 16 had a mild allergic reaction. What percent of the people had a mild allergic reaction
Answer:
0,2%
Step-by-step explanation:
16 / 8000 = 0,002
0,002 * 100 % = 0,2%
3: A farmer keeps cows and pigs on his farm. The ratio of cows to pigs on the farm is 2:3 (a) What percentage of the animals on the farm are cows? (b) What percentage of the animals on the farm are pigs?
Answer:
(a) 40% of the animals are cows.
(b) 60% of the animals are pigs.
Step-by-step explanation:
(a) You have to find the percent of the cows. 2:3 can be written as 2/5 for the cows and you have to figure out x/100.
2/5 = x/100
5*20 = 100
2*20 = x
40 = x
(b) The rest of the animals on the farm are pigs so you have to subtract 40 from 100 for the answer.
100-40 = y
60 = y
What is a scalar quantity ?
Answer:
A scalar quantity is defined as the physical quantity with only magnitude and no direction.
Solve for m
kx-bf=fy/m
Answer:
m=fy/kx-Bf
Step-by-step explanation:
you simply simplify the equitions to be left with m on one side
Convert an area 75000m2 to hectares
Answer:
10000m2 =1 hectare
75000m2 = 75000/10000 hectares
=75/10hectares
=7.5hectares
note:1 hectare =10 000m2
Hope this helps!!Need help will give brainleist
f(10) basically means when x =10 what is our y value
in this case Y= 5
Factor (x^2-9) (x^2-16)
Answer:
( x - 3 )( x + 3 ) ( x - 4 )( x + 4)
Step-by-step explanation:
( x^2 - 9 ) ( x^2 - 16 )
( x - 3 )( x + 3 ) ( x - 4 )( x + 4)
Hopefully this helps!
Brainliest please?
[tex](x^2 -9)(x^2 -16)\\\\=(x^2 -3^2)(x^2 -4^2)\\\\=(x+3)(x-3)(x+4)(x-4)[/tex]
Answer this Question I’ll BrainElist and PLEASE HELP ME DUE NOW PLEASE
Step-by-step explanation:
I I think you have your answer now
Write the number 0.000 000 7 in standard form.
Answer:
7 x 10^-7
Step-by-step explanation:
The number of data points from the box that fall in the interval of 10-15 is 21 25 25 26 19 24. 25 17 23 25 30 28 25 28 19 21 25 17 21 24 30 17 28 20 21
Answer:
I have no clue I'm trying to get my account set up
Cindy saves 420 each month her monthly salary is 2100 what is the ratio of the amount Cindy saves to the amount she earns each month?
the ratio of 2100 salary to 420 saved is 15:3 each month