An industrial process produces batches of a chemical whose impurity levels follwo a normal distribution with standard deviation 1.6 grams of chemical. A random sample of 100 batches is selected in order to estimate the population mean impurity level. The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Answer:
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation 1.6 grams of chemical. Random sample of 100.
This means that [tex]n = 100, s = \frac{1.6}{\sqrt{100}} = 0.16[/tex]
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by how much?
Z multiplied by s, in which Z has a p-value of 1 - 0.0367 = 0.9633, so Z = 1.79.
1.79*0.16 = 0.2864.
The probability is 0,0367 that the sample mean impurity level exceeds the population mean by 0.2864 grams of chemical.
4.000.000 x 4.000.000 = ?????
Helpp
I think the answer is 16 but I'm not 100% sure
Common ration of 54 and 72
Answer:
answer is 18 54 an 72 is 18
Which
expression iS equivalent to (a^8)^4
Answer:
Step-by-step explanation:
What are the nasser choices
Answer:
a^32.
Step-by-step explanation:
Using one of the laws indices:
(a^8)^4
= a^(8*4)
= a^32.
4 7/8 - 2 3/8 simplest form
Answer:
2 1/2
Step-by-step explanation:
4 7/8= 39/8
2 2/8= 19/8
39/8 - 19/8 = 20/8 = 2 4/8 = 2 1/2
Which of the following is a benefit of doing business with an online bank?
A. Greater variety of services
B. Personalized service
Ο Ο
C. Variety of deposit locations
O
D. Typically higher savings rates
Sara drives 72 miles on 3.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 12.3 gallons of gas?
Answer:
276.75 miles
Step-by-step explanation:
12.3/3.2 × 72 = 276.75 miles
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Answer:
2310 ways
Step-by-step explanation:
We are given;
Number of cans = 11
Number of cans of corn = 4
Number of cans of peas = 1
Number of cans of beets = 6
Following the rule of combination and permutations and applying it to this question, we have;
Number of ways = 11!/(6! × 1! × 4!)
Number of ways = 2310 ways
Records show that 12% of all college students are foreign students who also smoke. It is also known that 40% of all foreign college students smoke. What percent of the students at this university are foreign
Answer: the percent of the students at this university are foreign = 30%
Step-by-step explanation:
Given: Probability that college students are foreign students who also smoke: P(S|F)=0.12
Probability that foreign college students smoke P(S∩F)=0.4
The probability that the students at this university are foreign :
[tex]P(F)=\dfrac{P(S\cap F)}{P(S|F)}[/tex] [By conditional probability formula]
[tex]=\dfrac{0.12}{0.4}\\\\=0.3[/tex]
Hence, the percent of the students at this university are foreign = 30%
How many numbers are there from x to 7x-8
Answer:
6x + 7
Step-by-step explanation:
7x - 8 - x
=>6x - 8
=> 6x - 8 + 1 (including x as number)
=>6x + 7
There are numbers in between (x) to (7x - 8), as per linear equation.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."
Given two numbers are (x) and (7x - 8).
Therefore, total numbers in between (x) and (7x - 8) are:
= (7x - 8) - x + 1
= 6x - 7
Learn more about a linear equation here: https://brainly.com/question/20363253
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Translate this sentence into an equation.
60 is the sum of 15 and Mabel's age.
Use the variable m to represent Mabel's age.
Answer:
60 = 15+m
Step-by-step explanation:
sum is the outcome or total of an addition problem
What is the distance between T(9, −5) and the center of the circle with equation (x – 6)2 + (y + 1)2 =10?
Step-by-step explanation:
first, determine the coordinates values like x =9 and y=-5
so x-6 =3
A factory produces 2985 bulbs in a day. how many bulbs did it produce in that year.
Answer:
1089525
Step-by-step explanation:
2985 is per day of bulbs and a year has 365 days
so we multiply bulbs by day and days in a year
which will give us 1089525
Find the exact value of sec A in simplest radical form
Answer:
sec A = sqrt(61) / 6
Step-by-step explanation:
sec theta = hypotenuse / adjacent side
sec A = sqrt(61) / 6
Answer this question to receive 10 points
Answer:
153.86.
Step-by-step explanation:
Use the formula pi times radius squared.
Do you think someone would steal a led light controller???
Cause it was lost yesterday at night in my room when my friends where over but the day before it was they’re?
Does it sound like we lost it our they stole it?
Answer ASAP
Answer:
yeah dude they might of. First look around everywhere in ur room before accusing them.
Step-by-step explanation:
good luck
Find (x,y) such that (8,2)(x,y) = (28,22)
Answer:
(x,y) = (3.5, 11)
Step-by-step explanation:
(8,2)(x,y) = (28,22)
Dot product, so:
[tex](8,2)(x,y) = (8x,2y) = (28,22)[/tex]
Then
[tex]8x = 28[/tex]
[tex]x = \frac{28}{8} = 3.5[/tex]
And
[tex]2y = 22[/tex]
[tex]y = \frac{22}{2} = 11[/tex]
So
(x,y) = (3.5, 11)
If the profits in your consulting business increase by 6% one year and decrease by 3% the following year, your profits are up by 3% over two years
Answer:
its 1.388 p
Step-by-step explanation:
i hope this helps
HELP WITH MY MATH PLEASEEE
Answer:
x = 18
Step-by-step explanation:
JM = LM
8x - 3 = 141
8x = 141 + 3
8x = 144
x = 144/8
x = 18
Answer:
since its a square each side is equal so
8x-3=141
8x=144
x=18
so
A: x=18
Hope This Helps!!!
What is the first step to solve the equation 12z - 21 = 92?
12z - 21 = 92
12z - 21 + 21 = 92 + 21
12z = 113
z = 113/12
Write the quadratic equation whose roots are - 6 and -4, and whose leading coefficient is 4.
(Use the letter x to represent the variable.)
Answer:
Step-by-step explanation:
y=4(x+6)(x+4)
y=4(x^2+10x+24)
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Match each expression on the left with its equivalent on the right. Some answer choices on the right will not be used.
Answer:
8200 * 100 = 820,00
820,000 ÷ 10 = 82,000
820 * 10 = 8200
82,000 ÷ 1,000 = 82
Step-by-step explanation:
Love your username btw
Arithmetic operations contain operations such as Addition, Subtraction, Multiplication, and Division.
What is meant by arithmetic operations?Arithmetic operations exist as a branch of mathematics, that concerns the analysis of numbers and operation of numbers that exist valid in all the other constituents of mathematics. It essentially contains arithmetic operations such as Addition, Subtraction, Multiplication, and Division.
8200 [tex]*[/tex]100 = 8,20,000
820000 ÷ 10 = 82,000
820 [tex]*[/tex] 10 = 8,200
82000 ÷ 1000 = 82
To learn more about arithmetic operations
https://brainly.com/question/26176335
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NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
A private university is accepting applications for enrollment.Out of 2,000 applicants,950 meet the GPA requirements,600 volunteer for community service,and 250 both meet the GPA requirements and volunteer.Which statement correctly describes the probability that an applicant meets the GPA requirements or volunteers?
A: Because some applicants volunteer and meet the GPA requirements, the events are mutually exclusive.Thus, the probability is 65%.
B: Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 65%.
C: Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 77.5%.
D: Because no applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 77.5%.
Answer:
It is B - Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 65%.
>3
Answer: Choice B
Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.
Thus, the probability is 65%.
====================================================
Explanation:
950 people meet the GPA requirements. Also, 250 both meet the GPA requirements and volunteer. This must mean 950-250 = 700 people only meet the GPA requirements, but don't volunteer. Let A = 700.
600 people volunteer. 250 both meet the GPA requirements and volunteer. This must mean 600-250 = 350 people volunteer only (ie they don't meet the GPA requirements). Let B = 350
Let C = 250 to represent the number who meet the GPA requirements and volunteer.
-----------------
In summary we found that,
A = 700 people meet the GPA requirements only (they don't volunteer)B = 350 people volunteer only (they don't meet the GPA requirements)C = 250 people both meet the GPA requirements and volunteerThat means A+B+C = 700+350+250 = 1300 people either meet the GPA requirements, volunteer, or both. This is out of 2000 people
1300/2000 = 13/20 = 0.65 = 65%
That calculation tells us that 65% of the 2000 applicants fit the conditions we're after. So that's the probability of randomly selecting someone to fit those conditions.
Because the value of C is not zero, this means we don't have mutually exclusive events. It's possible that someone fits both criteria. Mutually exclusive events cannot happen at the same time.
In other words, if we did have mutually exclusive events, then someone couldn't both meet the GPA requirements and volunteer at the same time (they would have to pick one or the other but not both).
7
10
6
What is the area of the triangle shown above?
Answer:
Area of triangle = 0.5* base * height
A = 0.5*6*10
A = 30
Help me thanks If you can
8. 5, 6, 3, -5
9. Winter, Colder
10. 5, 6, 10, 12, 7
11. Units squared and Units cubed, the difference is that with cubed you're getting the area of three planes instead of two.
plaz..mmnj k,mnmnm 1
Answer:
Option 1
Step-by-step explanation:
3x - 7y = -7y + 3x
They have simply been moved to opposite ends of the equation.
Find the area of this semi-circle with radius,
r
= 15cm.
Give your answer rounded to 1 DP.
Answer:
Semicircle = 353.25 cm²
Step-by-step explanation:
Area of semicircle = πr²/2
substitute the values
semi circle = 3.14 × 15 × 15 / 2
Area of semicircle = 353.25 cm²
Is 256.78 power by 10 100 or 1000
Answer:
I would say 100 since 256.78 is closer to 100 then 1000 or 10
Step-by-step explanation:
During the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?
Answer:
After three months the value of the food bill will be $ 224.64.
Step-by-step explanation:
Given that during the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month, for state whether this increase was linear or exponential, and determine, if your food bill was $ 130 in one month during this period, what was it three months later, the following calculations must be performed:
A hyperinflation raises prices exponentially (the percentage is calculated based on the increase of the previous month). Thus, to calculate the price of the food bill, the following calculation must be performed:
130 x 1.20 ^ 3 = X
130 x 1.728 = X
224.64 = X
Therefore, after three months the value of the food bill will be $ 224.64.
Erin has 5 cans of juice and drinks 1/3 of a can daily. in how many days will she empty all the cans she has? I think it's 1/15 I'm not sure though.