Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) (a) What is the (approximate) probability that X is at most 30
Answer:
0.9726 = 97.26% approximate probability that X is at most 30
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).
This means that [tex]p = 0.11[/tex]
Random sample of 200 shafts
This means that [tex]n = 200[/tex]
Mean and Standard deviation:
[tex]\mu = E(x) = np = 200*0.11 = 22[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.11*0.89} = 4.42[/tex]
(a) What is the (approximate) probability that X is at most 30
Using continuity correction, this is [tex]P(X \leq 30 + 0.5) = P(X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 22}{4.42}[/tex]
[tex]Z = 1.92[/tex]
[tex]Z = 1.92[/tex] has a pvalue of 0.9726.
0.9726 = 97.26% approximate probability that X is at most 30
Arithmetic question: You need to serve 58 people, 2 slices of pizza each. (Each pizza will be cut into 12 slices each.) (1) How many pieces of pizza do you need altogether? Identify the original improper fraction (or its reduced form) needed to solve this problem. Calculate the solution to give a mixed number answer? (2) How many pizzas do you need to order and how many extra slices will you have? Show any work needed to answer questions.
Answer:
5 order pizza
Step-by-step explanation:
12+12+12+12+12=60 I have 2 extra pizza
NEED HELP ASAP PLEASE HELP
Answer:
the second one or b. :)
Step-by-step explanation:
At the end of August, a store is
trying to get rid of their swimsuits to
make room for fall clothes The
price of a swimsuit is reduced $5
each week for 6 weeks By how
much did the price of the swimsuit
change during this time?
Answer:
Week one: 5$ off
Week two: 10$ off
Week three: 15$ off
Week four: 20$ off
Week five: 25$ off
Week six: 30$ off
30-5=25 There is a 25 dollar difference from week one and week six
Step-by-step explanation:
Which strategy uses place value to correctly solve for 321 x 4?
Answer:
300x4 =1200
20x4 = 80
1x4 =8
1288
Step-by-step explanation:
Break apart 321 = 300+20+ 1
This is the hundreds, tens, and ones
Then multiply each by 4
Add all together to get answer
The slope through (3, 5) and (1. y) is 3. Find y.
Really need this answer!
Step-by-step explanation:
y2 - y1 / x2 - x1
2 = 5 - y / (3 - 1)
4 = 5 - y
y = 1
So the line with slope 2 passes through the points (1,1) and (3,5).
Hope this helps!
what is 9+2 I WILL MARK BRAINIEST
Answer:
11 ! have a great dayy:) !
Randy has 53 inches of ribbon that he cuts into 6 pieces of equal length. What is the equal length of each piece of ribbon in inches
Answer:
9
Step-by-step explanation:
The reason being 9 is because the keyword was equally so if you need to add an additional inch, it will make it equal.
Which of these equations are true when the value of y is 27?
I. −9 + y = 18
II. −18 + y = −45
III. 5y = 135
IV. 2y = 29
Answer:
I. -9 + y = 18
Step-by-step explanation:
Double-check to see if I was correct
The equations I. and III. satisfies the condition when y = 27
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 ,
The value of y = 27
So , substituting the value of y in all of the given equations , we get
I.
-9 + y = 18
when y = 27
Substituting the value of y , we get
-9 + 27 = 18
18 = 18
So , I. satisfies the condition and the equation is TRUE
II.
-18 + y = 45
when y = 27
Substituting the value of y , we get
-18 + 27 = 45
9 ≠ 45
So , II. does not satisfy the condition and the equation is FALSE
III.
5y = 135
when y = 27
Substituting the value of y , we get
5 x 27 = 135
135 = 135
So , III. satisfies the condition and the equation is TRUE
IV.
2y = 49
when y = 27
Substituting the value of y , we get
2 x 27 = 29
54 ≠ 29
So , IV. does not satisfy the condition and the equation is FALSE
Hence , the equations I. and III. are TRUE
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for which set of problilities would events a and b be independent
Answer:
Events A and B are independent if and only if P(A and B) = P(A)P(B). If you know these probabilities, you can check to see if this holds.
Step-by-step explanation:
:)
Find the probability of 5 successes in 9 trials of a
binomial experiment in which the probability of
success in any one trial is 37%.
Round to the nearest tenth of a percent.
Dora and boots are decorating cupcakes for a bake sale. Dora already has 25 cupcakes decorated and can decorate 10 cupcakes per hour. Boots has no cupcakes decorated yet but can decorate 15 cupcakes per hour. When will Dora and boots have the same number of cupcakes decorated and how many will they have
Answer: after 5 hours, 75 cupcakes
Step-by-step explanation:
Use mental math, estimation, and the division algorithm to evaluate the expressions.
What is the answer ?
118.4 divided by 6.4 ?
Answer:
18.5
Step-by-step explanation:
Your answer
1 point
Practice Question #7: There are 24 students in Ms. Watters Social Studies
class. 5/8 of these students earned an A on the geography unit
assessment. How many students earned an A? (enter only the number) *
Is height always a statistical subject
Answer:
It Is!
Step-by-step explanation:
"For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages."
Exercise 4.3. Determine the exact probability of drawing a 10 from a shuffled pinochle deck. (In a pinochle deck, there are 48 cards. There are six values: 9, 10, Jack, Queen, King, Ace. There are two copies of each value in each of the standard four suits: hearts, diamonds, clubs, spades.)
Answer:
[tex]\frac{1}{6}[/tex] probability of drawing a 10 from a shuffled pinochle deck.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Total of 48 cards.
Of those, there are 2*4 = 8 cards that are 10. So
[tex]p = \frac{8}{48} = \frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] probability of drawing a 10 from a shuffled pinochle deck.
help please! look at question
What is the distance between the points(-2, 1) and (1, 3)? Round answer to the nearest tenth.
Answer:
.
Step-by-step explanation:
2 × (8 + 16 ÷ 8) − 3
2*(8+16/8)-3
= 2*(8+2)-3
2*10-3
20-3
17
The ground temperature at airport is 12 degrees. The temperature decreases by 5.2 degrees for every mile above ground. What would be temperature outside plane located at 3 miles above the airport
Answer:
The outside plane located at 3 miles above the airport is of -3.6 degrees.
Step-by-step explanation:
The ground temperature at airport is 12 degrees. The temperature decreases by 5.2 degrees for every mile above ground.
This means that the temperature in n miles above ground is given by:
[tex]T(n) = 12 - 5.2n[/tex]
What would be temperature outside plane located at 3 miles above the airport
This is T(3). So
[tex]T(3) = 12 - 5.2*3 = 12 - 15.6 = -3.6[/tex]
The outside plane located at 3 miles above the airport is of -3.6 degrees.
which of the following graphs describes the solution set of -4/5x-13/5>=-9?
Answer:
Hey Bud
your answer is x ≤ 8
Step-by-step explanation:
should be closed dot pointing to the negative numbers
Let's solve your inequality step-by-step
Step 1: Simplify both sides of the inequality.
Step 2: Add 13/5 to both sides.
Step 3: Multiply both sides by 5/(-4).
Can someone HELP ME please!!?
What is Max’s final number of his number if his starting number is 7?
Answer:
30
Step-by-step explanation:
(n+8)=2(7+8)=2(15)=30
Answer:
30
Step-by-step explanation:
I need help to find the range
Answer:
algebraic terms = 4- -4 = 8
Step-by-step explanation:
-4 is our lowest value as 5 is not equal or counted
4 is our highest value and is counted.
Pls help me this is 7th grade (ADVANCED)
Answer:
Step-by-step explanation:
Any line will add up to 180 degrees. If you subtract the 165 degrees from 180 (total), you will get the x value.
180 - 165 = 15 degrees
Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.
Which explicit formula can be used to model the same sequence?
f(x) = 12(4)x
f(x) = 3(4)x − 1
f(x) = 4(12)x
f(x) = 4(3)x − 1
Answer:
B
Step-by-step explanation:
I got u
The explicit formula for the geometric progression is f ( x ) = 3 ( 4 )ˣ⁻¹
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
f ( x + 1 ) = 4 f ( x )
where the second term is a₂ = 12
Now , the explicit formula is given by
f ( x ) = 3 ( 4 )ˣ⁻¹
when x = 2
f ( 2 ) = 3 ( 4 )²⁻¹
f ( 2 ) = 3 ( 4 )
f ( 2 ) = 12
Hence , the GP is f ( x ) = 3 ( 4 )ˣ⁻¹
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Which of the following graphs represents the solution to the following system
of inequalities?
3x + 4y <12
2x - y24
Answer:
I am pretty sure it is most likely answer D.
Step-by-step explanation:
Hope this helps! Have a great day and good luck!
Evaluate the following expression if x=4 28x - 9 (2x+ 6)
Answer:
-14
Step-by-step explanation:
substitute 4 for x
28(4) - 9 (2(4)+ 6)
multiply
112-9(8+6)
add numbers
112-9(14)
multiply
112-126
subtract
-14
Identify the kind of sample that is described. A researcher asked a simple random sample of home-schooled children, a simple random sample of children who attend private school, and a simple random sample of children who attend public school their opinion on the new town curfew.
Answer:
stratified sample
Step-by-step explanation:
The kind of sample that is being described is known as a stratified sample. This would be the type of sample because the researchers are dividing the entire student population that exists into various different categories or groups. The groups that have been created are home-schooled students, private school students, and public school students. All of the students are still part of the student population and therefore represent their groups.
which of the following is the slope of the line that passes through the points (-2,8) and (10,-1)